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Defender John Stones bagged a brace of headed goals and Brazilian forward Gabriel Jesus netted the other as City inflicted the heaviest-ever home defeat in UEFA club football on the Dutch champions and former European Cup holders.
Aguero reached his milestone with a typically clinical finish from Kyle Walker’s cross as City made a fast start to the game, scoring three times in the opening 25 minutes to stun their hosts and kill off the contest.
Feyenoord, playing in the group stages of the Champions League for the first time in 15 years, never seriously troubled City goalkeeper Ederson who had recovered sufficiently to play, albeit with a rugby-style scrum cap, after receiving a boot to the face from Liverpool’s Sadio Mane in a 5-0 Premier League win on Saturday.
Spurs win on back of Kane double
Harry Kane struck twice as Tottenham Hotspur made a flying start to their Champions League campaign with a 3-1 win over Borussia Dortmund.
The England striker made sure there was no repeat of last season's home woes in the competition with his side's second and third goals after Dortmund's Andriy Yarmolenko had cancelled out Son Heung-min's opener in a frantic start.
Kane had failed to score in August before scoring twice against Everton at the weekend and showed he was back to his lethal best with a fine left-foot finish in the 15th minute.
He then slotted his second on the hour mark to seal only Tottenham's third win in 13 matches at Wembley where they lost two of their three Champions League home games last season.
The only blemish on the night for Spurs was centre back Jan Vertonghen's dismissal in stoppage time.
Liverpool held to draw
Liverpool paid a heavy price for a first-half penalty miss as Sevilla grabbed a late equaliser to earn a 2-2 draw in their Champions Leagu opener at Anfield.
The Premier League side had been cruising after overcoming the shock of Wissam Ben Yedder's fifth-minute goal to lead 2-1 at halftime.
But Roberto Firmino, who had scored Liverpool's first on 21 minutes, struck a post with a penalty just before the break, shortly after Mohamed Salah had put them ahead.
Despite Liverpool dominating the second period, it was Sevilla who scored through Joaquin Correa.
Philippe Coutinho received a standing ovation from the Anfield faithful when he appeared as a substitute on 76 minutes for his first appearance since asking for a transfer, while Liverpool's Joe Gomez was sent off for a second booking in stoppage time.