A day after City manager Roberto Mancini suggested Chelsea's title defence would be a cruise, his side begged to differ and clinched victory thanks to Tevez's 59th minute solo goal, his fourth in his last three matches against Chelsea.
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Arsenal could not capitalise on defeat for their London rivals, however, as they surprisingly went down 3-2 at home to West Bromwich Albion despite two late goals from Samir Nasri.
Chelsea, who failed to score in the league for the first time since last December, are top with 15 points but Manchester United can cut the gap to a point if they beat Bolton Wanderers on Sunday.
Arsenal and City have 11 with West Brom fifth on 10.
Everton slumped to the foot of the table after a 0-0 stalemate at Fulham while the gloom at Anfield deepened as Liverpool drew 2-2 at home to Sunderland. After the match fans staged a sit-down protest against the club's American owners.
West Ham United moved off the bottom with their first victory of the season, beating visiting London rivals Tottenham Hotspur 1-0.
Blackpool lost 2-1 at home to Blackburn Rovers while Birmingham City versus Wigan Athletic ended scoreless.
Mancini's expensively assembled Manchester City side would have fallen 10 points adrift of Chelsea had they lost the lunchtime kick-off but the Italian won the tactical battle over compatriot Carlo Ancelotti who was critical of his players.
"We didn't play how we wanted," he told Sky Sports. "We weren't able to use our quality and were too complicated. City performed well in midfield and won a lot of tackles and they deserved to win."
SUBDUED CHELSEA
That said, City offered precious little in attack during the first half but importantly succeeded in subduing a Chelsea strikeforce that had laid waste to defences so far this season with 21 league goals in a rip-roaring five-match run.
Tevez was a peripheral figure as Chelsea looked the more likely side to break the deadlock but he provided one individual moment of real quality as the hour mark approached.
There seemed no danger when Yaya Toure received the ball in his own half and passed to Tevez but the Argentine was surprisingly allowed to run unimpeded towards the Chelsea goal.
He jinked to the right and lashed a shot through the legs of Ashley Cole and beyond Petr Cech's despairing dive.
Chelsea, for whom defender Branislav Ivanovic headed against the woodwork in the first half and Nicolas Anelka went close early in the second, never really looked like equalising and it was puzzling when Didier Drogba was substituted by Ancelotti.
"It was tactical, I felt we didn't have enough pace in the attacking half," the Chelsea manager said.
Arsenal had not lost at home to West Brom for 27 years but found themselves 3-0 down as the visitors, who also missed a first-half penalty at 0-0, scored through Peter Odemwingie, Gonzalo Jara and former Gunners player Jerome Thomas.
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