United left back Luke Shaw suffered what appeared to be a serious injury and was taken off on a stretcher with an oxygen mask strapped to his face in the early stages of the Group B game.
United's Memphis Depay returned to the club where he made his name and reminded spectators at the Philips Stadium of his prowess with a stunning 41st-minute opener.
PSV, however, caught the visitors napping at a corner in first-half stoppage time as Hector Moreno equalised before a swift break away set up the 57th-minute winner.
First loss for City
Juventus came from behind to hand Manchester City their first defeat this season as Mario Mandzukic and Alvaro Morata gave the Italian champions an opening 2-1 win in Group D.
Premier League leaders City were fortunate to go ahead after 57 minutes when Vincent Kompany, climbing all over Giorgio Chiellini, saw the defender head an own goal as the home skipper wheeled away to celebrate instead of being punished for a foul.
But Juve pulled level in the 70th minute when Mandzukic touched the ball in off the post after Paul Pogba sent in a high cross from the left.
It was the first goal City had conceded after five domestic league wins so far this term but worse followed when Morata scored with a 20-metre left-foot curler in the 81st minute to snatch all three points.
Ronaldo surpasses Messi
Cristiano Ronaldo moved three goals clear of Lionel Messi as the Champions League top scorer when he netted a hat-trick for Real Madrid in a 4-0 victory over 10-man Shakhtar Donetsk in their Group A opener.
A howler from Shakhtar goalkeeper Andriy Pyatov let in Karim Benzema to score the opener in the 30th minute before the visitors were reduced to 10 men five minutes into the second half when Taras Stepanenko hacked down Sergio Ramos and was shown a second yellow card.
Real doubled their lead after Ronaldo's shot hit Shakhtar captain Darijo Srna on the back in the 54th minute and the referee inexplicably awarded a penalty and the Portugal captain netted another spot kick nine minutes later after Marcio Azevedo handled in the area.
Ronaldo, who hit five past Espanyol in La Liga at the weekend, completed his hat-trick in the 81st minute when he followed up a Marcelo shot and headed into the net to take his Champions League tally to 80.
Real's victory gave new coach Rafa Benitez a winning debut but came at a cost as their Wales winger Gareth Bale limped off midway through the first half with what looked like a muscle strain in his left leg.
Real, the record 10-times winners and 2014 champions, several times went close in the early stages with Bale almost scoring with a clever flick through his legs from Dani Carvajal's cross in the 13th minute.
Shakhtar were holding their own reasonably well without troubling Real keeper Keylor Navas until Pyatov came out to gather a cross and fumbled the ball straight to Benzema.
The France striker, who missed two other relatively easy chances, cracked it into the empty net for his 43rd Champions League goal.
Real have only failed to win their opening home match twice in 45 European Cup campaigns and not since 1962 when they drew 3-3 against Anderlecht.
Benefica survive scare
Champions League debutants Astana gave Benfica some worrying moments as they held out until halftime and then hit the post before going down to a 2-0 defeat in their opening Group C match.
Nicolas Gaitan burst through the Astana defence to provide the breakthrough six minutes into the second half and Kostas Mitroglu made the points safe for the Eagles in front of a sparse crowd at the Stadium of Light.
But Astana, the first Kazakh team to reach the group stage, will have plenty of positives to reflect on as they make the 7,000 kilometre trip back to Central Asia.
The Kazakh champions kept Benfica at bay for the first 45 minute with some solid defending, plus two last-gasp saves by goalkeeper Nenad Eric who denied Jonas with his leg on both occasions.
In between, Benfica goalkeeper Julio Cesar gave home fans the jitters as he fumbled Foxi Kethevoama's curling free kick before gathering the ball at the second attempt.
Astana nearly took a sensational lead at the start at the second half when Aleksei Schetkin, who had just come on as a substitute, got between Jardel and Luisao to poke an effort against Julio Cesar's post.
Gaitan ended their resistance when he latched onto a loose ball, powered his way through a gap between the defenders and placed an angled shot past Eric in the far corner.
Mitroglu, having headed wide from eight metres, atoned for the miss when he turned in Eliseu's cross from close range following another move down the left in the 62nd minute to secure the points for the Portuguese champions.
Di Maria inspires PSG to win
Angel Di Maria brought his delicate touch to Paris St Germain's game as the French champions started their Champions League campaign with a routine 2-0 home win against Malmo.
Di Maria scored after four minutes of their Group A match and Edinson Cavani made it 2-0 with a 61st minute header in a one-way encounter at the Parc des Princes.
Playing against the club where he started his career, PSG forward Zlatan Ibrahimovic looked rusty, having played only one league game in an injury-plagued start to his season. He was replaced by Javier Pastore 15 minutes from time.
Malmo thought their moment had come in the 26th minute but Markus Rosenberg's goal was disallowed after the forward had fouled Thiago Silva.
Much of the build up to the match centered on Ibrahimovic facing his boyhood side, but the Swede, who missed the last league game because of an abdominal muscle injury, for once did not take the starring role.
That fell to Di Maria who shone, showing he has what it takes to lift PSG to the next level after the French champions were knocked out in the quarterfinals in the three previous editions.
The Argentine, brought in from Manchester United during the close season, beat the offside trap to collect Marco Verratti's pass on the right flank and from the inside the box, whipped the ball into the far top corner for his first PSG goal.
Malmo thought their moment had come in the 26th minute but Markus Rosenberg's goal was disallowed after the forward had fouled Thiago Silva.
Di Maria came close to doubling the tally but his long-range attempt shaved Johan Wiland's right post as PSG imposed their possessive pattern on the game.
Malmo, however, played tighter after the break but they still conceded another just after the hour when Cavani headed home after Maxwell's cross from the left had been deflected into his path by Ibrahimovic.
David Luiz, unmarked at the penalty spot, missed an opportunity to put the hammer down on the game, sending a header straight at Wiland from close range.
The visitors, however, had abandoned all hope and with the three points secured, coach Laurent Blanc substituted Di Maria, who received warm applause from the crowd, with Ezequiel Lavezzi coming on four minutes from time.
Sevilla score three in win
Europa League winners Sevilla scored two out of three penalties in the second half as they beat Borussia Moenchengladbach 3-0 in Champions League Group D.
Kevin Gameiro scored from the spot seconds after the restart but failed to do it again two minutes later, striking his second penalty against the crossbar.
Sevilla's Argentine Ever Banega made amends with their third spot kick in the 67th minute and Yevhen Konoplyanka wrapped up the win in the 84th with a clever shot from a tight angle that beat goalkeeper Yann Sommer.
Gladbach, who have made their worst start to a Bundesliga campaign with four consecutive defeats, were no match for the speedy Spaniards and struggled to contain them throughout the entire game.
Atletico Madrid claim away win
Two first-half goals from Antoine Griezmann gave Atletico Madrid a strong start to their Champions League campaign with a 2-0 away win over Galatasaray in their opening Group C fixture.
Griezmann put the visitors ahead in the 18th minute when Juanfran sent in a cross from the right and the French international fired the ball past an outstretched Fernando Muslera in the Galatasaray goal.
Atletico doubled their lead with a second goal from Griezmann in the 25th minute when Diego Godin headed a cross from Koke back across the goal for the winger to knock the ball into the net from close range.
The home side's goal opportunities were few in the first half. Atletico keeper Jan Oblak was tested in the 29th minute, pushing the ball behind for a corner after a long-range shot from Wesley Sneijder. Umut Bulut and Jason Denayer both had opportunities late in the first half but headed wide.
In the second half Galatasaray raised the pressure on the Atletico goal while Atletico sat back and focused on maintaining their lead.
Lukas Podolski shot wide from the edge of the penalty area in the 51st minute and Sneijder fired in a shot which missed the target two minutes later. An opportunity fell soon after to Selcuk Inan who also fired wide of the post.
But Atletico kept their lead intact despite the pressure and Griezmann had a chance to complete his hat-trick in the 86th minute but with only the keeper to beat, Muslera blocked his shot.
