The Argentinian striker took his tally for the season to 25 goals with a quickfire hat-trick against Wigan at Eastlands.
Tevez took full advantage after Latics defender Gary Caldwell was dismissed in the 55th minute for a challenge on him. Wigan felt aggrieved being a man down and more so as Tevez then went on to score his treble in double-quick time.
City, who now move above Liverpool and into fifth place, had most of the possession in the first half but couldn't make the breakthrough.
Emmanuel Adebayor, back in the team after a four-match suspension, got into a good position in the 10th minute, only for Titus Bramble to block his effort.
City kept up the pressure and almost went ahead a minute later when Shaun Wright-Phillips delivered the ball into the path of Tevez.
The Argentinian striker whipped in a shot but Vladimir Stojkovic made a stunning point-blank save and Bramble swept the ball to safety.
Wigan launched a swift counter attack in the 27th minute when Hugo Rodallega skipped past Kolo Toure with ease.
The striker was closed down by Wright-Phillips but rattled in a shot that Given turned around the post.
Back came City and Tevez raced past Mario Melchiot only to see his delicate chip from an acute angle go inches wide.
Wigan, however, continued to look dangerous going forward and Given pushed Paul Scharner's shot to safety after a free-kick from Marcelo Moreno had been deflected off the wall.
Scharner, who was covering a lot of ground, then cleared the bar with his effort in the 41st minute after good link up play between Rodallega and Moreno.
A minute later Tevez made a vain appeal for Caldwell to be punished for a challenge when little contact appeared to be made.
Mancini made one change at half-time in an attempt to break the deadlock, bringing on Craig Bellamy for Wright-Phillips.
Adebayor did find the net in the 47th minute but his effort was ruled out for offside after Stojkovic spilled Tevez's shot.
City had a claim for a penalty dismissed in the 52nd minute when Caldwell appeared to handle under pressure from Bellamy.
Play switched back down the other end and Rodallega squandered a great chance for Wigan.
He dragged a shot wide of the post after the ball had spun off the back of Pablo Zabaleta and Toure found himself out of position.
Wigan were reduced to 10 men in the 55th minute with former Celtic defender Caldwell handed a straight red card as he tried to win the ball off Tevez.
The visitors were furious with referee Stuart Attwell but they pulled themselves together and almost went ahead.
Moreno got the better of Toure and cut inside but his effort went marginally wide.
Tevez then made another unsuccessful appeal for a penalty following a challenge by Scharner.
City made the breakthrough in the 72nd minute after a mix up between Scharner and Stojkovic allowed Adebayor to get the slightest of touches in the penalty area.
That was enough to free Tevez, who made Wigan pay for their error with a clinical finish.
Adebayor should have added a second but Scharner made up ground before Tevez added a second in the 75th minute.
He scored at the back post after Vincent Kompany had flicked on a cross from Adam Johnson and completed his hat-trick in the 84th minute.
He skipped away from a tiring Scharner and Bramble to fire into the corner.