City's first victory since September did a huge favor for neighbour Manchester United, with the defending champions thrashing West Ham 4-0 to close the gap on Chelsea to two-points.
"We are disappointed because it was a tough game," said Chelsea manager Carlo Ancelotti, whose midfielder Frank Lampard missed a late penalty. "We started the game very well, but Manchester played a very strong and tough game."
Arsenal climbed to third by beating Stoke 2-0, Aston Villa moved up to fifth with a 3-0 victory over Hull, but Liverpool squandered another chance to keep up with the top four by drawing 0-0 at Blackburn.
In the battle against relegation, Portsmouth stayed bottom despite beating Burnley 2-0 and Wolverhampton moved above Bolton in the drop zone by beating Gary Megson's side 2-1. Birmingham continued its surge up the standings by winning 3-2 at Wigan to claim a third straight victory.
Manchester City got off to the worst possible start with Emmanuel Adebayor accidentally turning the ball into his own net after goalkeeper Shay Given had parried Nicolas Anelka's eighth-minute shot.
But the Togo striker made amends in the 37th when he tapped home the rebound from close range after his initial effort had bounced back off Chelsea captain John Terry.
As City pushed for a winner, Shaun Wright-Phillips won a free kick when he was fouled by Ricardo Carvalho. Tevez strode up and curled the ball around the defensive wall and beyond goalkeeper Petr Cech in the 56th.
Chelsea was handed lifeline when Nedum Onuoha fouled striker Didier Drogba late in the match, but Lampard's resulting penalty kick was saved by Shay Given.
At Upton Park, veteran United veteran Paul Scholes scored his 99th Premier League goal Saturday in the rout of West Ham.
The 35-year-old Scholes had indicated on the eve of the match that he could retire at the end of the season because of his failure to make "much of a contribution" to the team.
But the former England international rebutted his own criticism on the stroke of halftime with a trademark volley from 20m.
"It was a great goal to get and at an important time so we settled down," manager Alex Ferguson said. "Four-nil is a good scoreline away from home - good for the goal difference, good for the confidence."
Darron Gibson, Antonio Valencia and Wayne Rooney each scored in an 11-minute burst of goals in the second half.
United manager Alex Ferguson had been forced to field a makeshift defense due to injuries, with midfielder Darren Fletcher at right back. And when captain Gary Neville, playing at center back, limped off after 34 minutes with a groin injury, Michael Carrick was shifted into the back four.
United finished the match with 10 men after Wes Brown limped off and, with all three substitutes used, Giggs was deployed at left back.
Arsenal also overcame injury problems, with Eduardo da Silva the latest casualty after pulling out before kickoff with a muscle injury. That left Andrei Arshavin to lead the strike force.
Cesc Fabregas had an early penalty kick saved by Thomas Sorensen, but the Arsenal captain exchanged passes with Arshavin, who volleyed in the club's first domestic goal since November 7.
"I don't think he was a big fanatic to play centre forward but I'm convinced he can play there because he has good body power, good movement and technique," Arsenal manager Arsene Wenger said of Arshavin. "He made intelligent movements and it worked today."
Aaron Ramsey came off the bench in the second half to secure Arsenal's win, dribbling inside the box and flicking the ball past Sorensen.
At Ewood Park, Liverpool captain Steven Gerrard was unable to inspire the team in his 500th match as Rafa Benitez's side continued to struggle without injured striker Fernando Torres. Liverpool's best chance came when David Ngog hit the crossbar.
"We need to win in these situations," Benitez said. "We are getting better but we know we have to do better."
Aston Villa remains above Liverpool in fifth as goals from Richard Dunne, James Milner and John Carew clinched a comfortable win over Hull.
Avram Grant recorded a first win since taking charge of the Portsmouth team with goals from Hermann Hreidarsson and Aruna Dindane seeing off Burnley.
Jody Craddock and Nenad Milijas scored for Wolves to beat Bolton 2-1, while Sebastian Larsson's second goal was the decider as Birmingham triumphed at Wigan.
