JOIN USManchester teams on song
City's victory was their first in Europe's elite competition after they drew and lost in their only matches in the European Cup in 1968 and started this season's Champions League campaign with a draw against Napoli and a defeat at Bayern Munich.
A Carlos Marchena own goal just before halftime brought City level after Cani gave Villarreal the lead in the fourth minute but just as the game seemed headed for a stalemate, substitute Sergio Aguero got the winner three minutes into stoppage time.
City manager Roberto Mancini, a seriously unhappy man when Argentine striker Carlos Tevez allegedly refused to come off the bench against Bayern Munich three weeks ago, was absolutely ecstatic at the end after Aguero's last-gasp strike.
With Napoli and Bayern Munich drawing 1-1 at the San Paulo Stadium, the German side stay top of Group A with seven points, followed by the Italians (5), City (4) and Villarreal (0).
Napoli goalkeeper Morgan De Sanctis saved a penalty from Mario Gomez early in the second half as they salvaged a point after Toni Kroos put Bayern ahead in the second minute. Napoli equalised six minutes before halftime when Holger Badstuber deflected a Christian Maggio cross into his own net.
While City's result left them third in their group, United climbed to second in Group B after striker Wayne Rooney scored two penalties against the Romanian champions. However, United finished with 10 men after defender Nemanja Vidic, back in the side for the first time since an injury in August, was controversially sent off soon after they took the lead.
It was a far from easy win for United who laboured for long periods but Rooney, sent off playing for England in a Euro 2012 qualifier against Montenegro on his last trip to eastern Europe, made sure of the points with two well-struck penalties.
Vidic was unfortunate to be red-carded for what looked a clumsy rather than dangerous challenge on Gabriel Giurgiu but United manager Alex Ferguson said he could understand why the Serbia international was dismissed.
The Romanian champions had Milan Perendija sent off after receiving a second yellow card for a foul two minutes from time.
Benfica's 2-0 win at Basel, with goals from Brazilian Bruno Cesar and a superb freekick by Paraguayan Oscar Cardozo, secured a second straight away win and put them top of Group C on seven points followed by United (5), Basel (4) and Otelul (0). The only blot on Benfica's night was a late red card for Emerson and the sending off of coach Jorge Jesus for dissent.
Real Madrid, chasing a record-extending 10th European Cup triumph, were the night's highest scorers as they beat Olympique Lyon 4-0 at the Bernabeu for their third straight win in Group D.
Real were utterly dominant against a side that have given them problems in the past, but there was little doubt about the outcome on Tuesday once Karim Benzema had struck against his old club in the 19th minute. Sami Khedira (47th), Mesut Ozil (55th) and Sergio Ramos (81st) all scored as Lyon retreated into their shell, seemingly more concerned with avoiding a heavier defeat than trying to win the match.
Ajax Amsterdam were the other Group D winners, beating Dinamo Zagreb 2-0 in Croatia with their first goals of this season's competition from Derk Boerrigter and Christian Eriksen at either end of the second half as they moved into second spot. Real lead with nine points, Ajax and Lyon both have four and Dinamo Zagreb are looking at the exit door after three defeats.
Inter Milan moved to the top of Group B with Giampaolo Pazzini scoring in their 1-0 win at Lille while CSKA Moscow moved off the bottom by beating former leaders Trabzonspor 3-0 at home.