Tevez, 26, produced a moment of genius at the start of the second half to see the Blues grab three goals in the space of 20 minutes. The 4-3 result saw City reach the summit for at least 24 hours as neighbours Manchester United prepared to face Tottenham Hotspur on Sunday.
City manager Roberto Mancini wasted no time in introducing £27 million signing Edin Dzeko to the Premier League. The Bosnian was one of three changes to the side that drew 0-0 with Arsenal, as Micah Richards, Jo and James Milner made way for him, Aleksandar Kolarov and Adam Johnson.
Dzeko was picked as the central striker in attacking 4-3-3 formation. Tevez was pushed out to the wide left position to accommodate despite his 12 league goals this campaign.
For Wolves, boss Mick McCarthy made two forced alterations to the team that beat champions Chelsea 1-0. Stephen Ward was drafted in to replace the suspended George Elokobi at left-back and Manchester United youth product David Jones came into midfield for the injured Kevin Foley.
Skipper Karl Henry claimed a place on the substitute's bench after a lay-off due to knee ligament damage picked up against Blackpool in November.
A typically damp Manchester day ensured the players were steadily soaked once they emerged from the comfort of the changing rooms for kick-off. The weather had no effect on the visitors and they started the brighter.
From a punt from kick-off, Nenad Milijas drove wide of Joe Hart's right-post before Steven Fletcher wasted a glorious chance to cross when played into space in the fifth minute.
A slip on the half-way line by Nigel de Jong two minutes later saw Kevin Doyle hang a deep cross into the City box. A weak defensive header from Kolarov on the stretch fell to Matt Jarvis, but the winger's effort was only deflected wide for a corner.
Wolves' positive start was rewarded in comedic fashion in the 12th minute as Milijas poked home a scrappy opener on the goal-line. A quick free-kick from Stephen Hunt was worked to Jarvis via Doyle and his cross ricocheted into Kolo Toure's path.
The Ivorian's slack clearance bounced into centre-back partner Vincet Kompany and fell invitingly to the Serb. His initial shot was smothered by Hart before he bundled home at the second invitation.
City continued to flounder under the unremitting rainfall and Jarvis was prevented from doubling the lead in the 20th minute. The wideman was smartly picked out by Steven Fletcher, and in acres of space, he could only side foot his shot into the stretched out legs of Kolarov.
The body language of the two managers spoke volumes as the match hit the half-hour mark. Mancini cut a figure of frustration as he threw his arms in the air as his expensively assembled players looked more bargain basement.
For McCarthy, he played the role of sergeant major on the touchline. With the help of assistant Terry Connor, he cajoled his well drilled troops to hold the line and mount counter-attacks.
The Italian's presence soon saw a revival from City. First, Adam Johnson forced Wayne Hennessey to save with his feet on 31 minutes before Tevez decided to take proceedings by the scruff of the neck and shot narrowly over with the goalkeeper at full stretch moments later.
Mancini's men then struck level on 40 minutes as Kolo Toure redeemed himself from his earlier error. Johnson swept a corner from the left-hand side into the path of Kompany.
The Belgium international lightly nicked the ball to the back post and Toure sidefooted the ball through Jones' legs and into the net. Toure's intervention was just about deserved as City finally kicked into life in the final stage of the first half.
City's improvement exploded with a brace of goals as the second period began. After a spell of pressure, the ball broke to Tevez in the 49th minute and the Argentine was at his majestic best to put City ahead.
The striker picked up the ball on the edge of the Wolves penalty area and was surrounded by defenders. With a dip of the shoulder and lightning quick footwork, he left Christophe Berra, Richard Stearman and Hunt in his wake as he threw the Eastlands crowd to their feet as he cooly slotted past Hennessey.
Things were soon to get even better for the hosts as Yaya Toure finished a lightning quick move he started on the edge of his own area in the 54th minute. The Ivorian fired past Hennessey after a rapid, one-touch counter attack that involved Tevez and an assist for new boy Dzeko.
City weren't satisfied with just a 3-1 lead and Tevez was again on hand to add to their lead. The Argentine secured a brace when he nodded in a cross from compatriot Pablo Zabaleta in the 66th minute.
No sooner had the Blues finished celebrating, substitute and ex-Wolves centre-back Joleon Lescott unnecessarily flopped into the back of Doyle in the penalty box and referee Lee Mason pointed to the spot. The Irishman dusted himself off and sent Hart the wrong way to give the visitors a glimmer of hope.
City continued to try and breach the Wolves defence on the counter but were handed a nervous end to the game thanks to a Ronald Zubar header in the 86th minute. The right-back's effort was cleared by Nigel de Jong behind the line after a Geoffrey Mujangi Bia corner.
As Mancini nervously watched on from the touchline, City tried to run down the clock. Despite these efforts, an over-hot cross from Milijas saved the Blues blushes deep into injury-time.
Hearts were in mouths again as Mujangi Bia saw a shot deflect just wide of the wrong-footed Hart's goal. In a helter-skelter end, City replacement James Milner saw a shot cleared off the goal-line after he side-footed Hennessey.
A sense of relief was evident as Mason blew the final whistle to put the pressure on United ahead of their heavyweight clash with Spurs.