Winger Ashley Young put three-times European champions United ahead just before the hour mark and Javier Hernandez extended the lead five minutes from time as they showed they meant business in a competition they would rather not be in.
Their domestic title rivals Manchester City made it harder for themselves in Portugal by conceding in the first half against the run of play before an Alvaro Pereira own goal and a late Sergio Aguero strike put them on course for the next round.
Other teams to build a solid advantage ahead of next week's second legs were Ukrainian side Metalist Kharkiv who won 4-0 at Salzburg and Atletico Madrid who take back to Spain a 3-1 win over Lazio after fighting back from a goal down.
The 2004 winners of the UEFA Cup - the Europa League's predecessor - Valencia secured a 1-0 win at Stoke City to sit pretty halfway through the tie while Twente Enschede came away with the same scoreline from Steaua Bucharest on a cold night.
Schalke 04 were glad to grab an equaliser 15 minutes from time to draw 1-1 at Viktoria Plzen, while Legia Warsaw's tie with Sporting was also evenly balanced after a 2-2 draw in Poland and Udinese and PAOK Salonika played out a 0-0 draw.
German side Hanover 96 needed an 80th-minute penalty by Jan Schlaudraff to complete a comeback at home to Club Bruges who had taken the lead early in the second half through Maxime Lestienne before Arthur Sobiech's equaliser.
Wisla Krakow, who played more than an hour with 10 men after Michal Czekaj was sent off, left it even later to snatch a 1-1 draw at home to Standard Liege with Tsvetan Genkov netting in the 88th minute.
In the day's other games, AZ Alkmaar beat Anderlecht 1-0 courtesy of Adam Maher's 35th-minute goal, Lokomotiv Moscow came from behind to overcome Athletic Bilbao 2-1 and PSV Eindhoven held on to an early two-goal lead to win 2-1 at Trabzonspor.
With the Europa League something of a consolation prize for teams who were eliminated from the elite Champions League at the group stage, the presence of heavyweights Manchester United and mega-rich Manchester City has injected it with a bit of glamour.
Having won seven European Cups between them, United and Ajax could easily have been meeting in the Champions League rather than the Thursday sideshow.
United manager Alex Ferguson, whose club have never won this competition or its predecessor, named a strong team to back up his pre-match assertions they were taking it seriously but their first-half performance lacked a cutting edge.
The English champions picked up the pace after the break and made the breakthrough when Nani's cross eventually found Young in space and the England winger took his time to pick his spot through the legs of keeper Kenneth Vermeer.
Ajax had their chances but United keeper David de Gea kept the four-times European champions at bay with some excellent saves, including one at full stretch from Siem de Jong's curling shot in the first half.
United made absolutely sure they left the Netherlands in the driving seat when substitute Antonio Valencia broke to feed Hernandez, who exchanged passes with Wayne Rooney before slotting home on 85 minutes.
"I'm delighted with the scoreline but I think it was a very ordinary performance by us, we didn't reach any great heights in the game but we did improve in the second half and we probably deserved to win it," manager Alex Ferguson told Channel Five.
"At home at Old Trafford (for the second leg) the opportunity to get through is a big one."
United are playing in the European second tier for the first time since 1995, while City are more familiar with the Europa League, having reached the last-16 last term.
Roberto Mancini's men learned from some of their mistakes of last season and forced home keeper Helton into a series of saves in a lively start at Porto.
The hosts took the lead when Hulk sent in a low cross that Silvestre Varela guided in on 27 minutes but City refused to be put off as they sat deep and tried to catch Porto on the break.
Balotelli had an excellent chance to soon afterwards when he found himself with space after the ball was played over the top but his shot from the edge of the area was saved by Helton.
The Italian was involved when Porto gifted their visitors a 55th-minute equaliser as Pereira sent the ball into his own net under pressure from Balotelli after a long ball from Yaya Toure.
Toure, making a welcome return after several weeks on duty with Ivory Coast at the African Nations Cup, then set up the winner five minutes from time when he rolled the ball into the path of Aguero who tapped in to make it two valuable away goals.
