The win at Wolves was City's first on the road since they won at Portsmouth on August 30.
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Tevez took his tally for the season to 12 - with eight of them coming in the last seven games.
His first was a somewhat fortuitous deflected 33rd-minute opener before he completed the scoring from the edge of the area four minutes from time.
Substitute Javier Garrido, who hadn't figured at all under Mark Hughes this season, had effectively made the game safe with a controversial 69th-minute free-kick.
The victory moves City to within two points of fourth-placed Tottenham and leaves Wolves firmly in the battle for survival.
A run of three wins in four games had seen Wolves surge out of the relegation zone. But back-to-back defeats against Liverpool and City has seen them slide back to within two points of the drop-zone.
Wolves enjoyed more than enough possession but lacked the decisive finishing touch to make that pay - and found their luck was out as well.
Their best spell came in the opening 20 minutes of the second half when Chris Iwelumo saw his shot deflected over the bar and Kevin Doyle was denied by his fellow Irishman Shay Given.
Craig Bellamy should really have given City the lead on the half-hour when Wolves failed to deal with a cross from Martin Petrov.
Tevez collected the centre and saw his cross deflected into the path of Bellamy who somehow lifted the ball over the bar from just six yards.
It was a glaring miss by the Welshman but he made amends just three minutes later by turning creator to tee up Tevez.
There was, however, a huge slice of luck about Tevez's goal. He was picked out by Bellamy's cross and his shot looked to be covered by goalkeeper Marcus Hahnemann.
But it took a huge deflection off Wolves central defender Christophe Berra to leave the stranded Hahnemann hopelessly wrong-footed.
Having shown his predatory instincts in front of goal, Tevez then came to the rescue of City at the other end of the pitch by clearing George Elokobi's 44th-minute header off the line following a corner from Kevin Foley.
Wolves had to carry out a defensive reshuffle at half-time after Berra was knocked temporarily unconscious following a heavy fall after a challenge on Bellamy and was replaced by Richard Stearman.
They were still getting to grips with that change when Bellamy should have made the game safe in the 48th minute.
Bellamy beat the offside trap to chase down a pass from Petrov only to slide his angled shot wide when he only had Hahnemann to beat.
Fortunately for City, it did not prove to be an expensive miss thanks to Garrido's neat finish from 20 yards.
But if Wolves felt hard done by after Tevez's deflected strike, they were positively fuming when Garrido struck.
Before Michael Mancienne fouled Gareth Barry 20 yards from goal to give away the free-kick, Wolves felt the game should have been halted as Bellamy was offside.
When Tevez was flagged offside 60 seconds later a seething Hahnemann threw the ball at the linesman to earn himself a booking and sum up a frustrating night for Wolves.
Tevez then gave the final scoreline a resounding look when he collected a cross-field ball from Robinho and drilled a low shot past Hahnemann.