Substitute Edin Dzeko scored twice in the final ten minutes to earn ten-man Manchester City a last-gasp 2-1 victory over West Bromwich Albion at The Hawthorns.
It looked set to be another disappointing day in City's stuttering title defence when James Milner was sent off for fouling Shane Long as the last man in the 23rd minute and Long gave the hosts the lead 67 minutes in.
Dzeko only entered the fray in the 79th minute but immediately tied things up and two minutes into added time he converted Sergio Aguero's pass for an unlikely three points.
City coach David Platt said: "It was tremendous how we stuck together in the second half and created so many chances. It's a great fillip to win after playing for almost 70 minutes with ten men."
United see off Stoke
Manchester United pegged Chelsea's lead at four points despite trailing Stoke City early on to a Wayne Rooney own goal. The striker was in the wrong place in the 11th minute as he diverted Charlie Adam's free-kick into his own net but he made amends with his first Premier League goal of the season to level up 16 minutes later.
It was a straightforward header from Rooney from a lovely Robin van Persie cross, and the Dutchman made it 2-1 to United with a goal a minute before half-time.
Danny Welbeck grabbed a third just after half-time and, although Michael Kightly gave Stoke hope with a solo effort in the 58th minute, Rooney made it 4-2 seven minutes later.
United manager Sir Alex Ferguson said: "Most of the games at home this season we've had terrible starts. When we did get going we played some terrific football. I was pleased with the performance after the first 20 minutes."
Liverpool managed their first home win of the season, 1-0 against struggling Reading, courtesy of a first Premier League goal from 17-year-old Raheem Sterling.
The teenager became the eighth youngest goalscorer in Premier League history when he netted in the 29th minute and the youngest Liverpool scorer since Michael Owen.
Hammers thrash Saints
Southampton's leaky defence cost them again as West Ham United raced to a 4-1 victory at Upton Park, with all the goals coming in the second half.
It took the hosts less than three minutes of the second half to take control, Mark Noble and Kevin Nolan netting, but Adam Lallana pegged them back in the 63rd minute.
However, Jose Fonte handled in the 72nd minute to give Noble the chance of a second from the spot before Modibo Maiga scored his first Premier League goal three minutes from time.
Two out-of-form teams met at the Liberty Stadium and it was Swansea City who ended their five-game winless run with a 2-1 victory over Wigan Athletic.
Pablo Hernandez broke the deadlock in the 65th minute and Michu added a second two minutes later. Emmerson Boyce netted with a neat backheel to make it three goals in five minutes but Wigan could not find an equaliser.
It was a quiet afternoon at Craven Cottage for 84 minutes but Chris Baird ensured it was Fulham who took the three points with a 1-0 victory over Aston Villa.