Manchester United's failure to hold onto a two-goal lead against Everton earlier in the day saw City's fate placed back in their own hands and the pretenders to the throne moved three points behind their great rivals ahead of the Manchester derby at the Etihad Stadium on April 30, when they can go top of the table on goal difference if they win.
Sergio Aguero opened the scoring at a roan-soaked Molineux with a neat finish against a Wolves side that suffered a ninth successive home defeat to confirm their relegation back to the Championship after a three-year stay in the top flight.
Samir Nasri doubled City's lead with 16 minutes remaining to compound the misery of Terry Connor, who has now collected just two points in nine games since the decision to replace Mick McCarthy as Wolves manager in February.
But his opposite number, who showed his frustration at times during an unconvincing second-half performance, was able to savour a result that means City will secure the title if they can win their final three games of the campaign.
City made one change from the side that defeated Norwich City 6-1 last weekend and it was an attacking one, with Yaya Toure replacing Nigel de Jong in the centre of midfield. Meanwhile, Dorus de Vries made his debut for Wolves following an injury to established goalkeeper Wayne Hennessey.
The suspicion that the Dutchman would be overworked on debut was only reinforced when Carlos Tevez enjoyed the first chance of the game inside 16 seconds, the striker driving a firm effort over the bar following a pass from Pablo Zabaleta.
But despite a run of eight successive home defeats, and a vast disparity in quality between the two teams, Wolves looked full of intent early on. Sebastien Bassong saw an effort deflected narrowly wide following a corner while Joe Hart pulled off a fine reaction save to tip a thunderous drive from David Davis round the post.
For all Wolves' early endeavour, though, City soon sought to take control of the tie and tried to free the lively Aguero, operating as part of a fluid attack, at every opportunity. After only seven minutes the Argentina international almost opened the scoring as he collected a ball over the top from Gael Clichy to the left of the box and made a dart forward before dragging his shot across goal and just wide of the far post.
The Argentina international should have done better when a misdirected header from Richard Stearman dropped into his path but his first-time effort with the outside of his boot dribbled wide when he could have taken a touch, spun and tested the vulnerable De Vries. Minutes later he made space with a quick touch on the edge of the box following good work from David Silva and Carlos Tevez before drilling another shot wide of the post.
With Nasri also contriving to fire wide following a glorious passing move that culminated in a fine through-ball from Zabaleta, it appeared as though the impotence that has afflicted City's away performances this season was affecting Mancini's side yet again.
However, Aguero exploited a moment of genuine class from Clichy to put City in front after 27 minutes. The French left-back skipped away from Michael Kightly before bending a glorious pass into the path of Aguero, who took a touch and stabbed the ball past De Vries from close range. It was the 12 time that either Aguero or Tevez had scored in the five games they had started together.
City were unable to press home their advantage as the second half restarted and after Steven Fletcher forced Hart into a fine save when beating Yaya Toure to a header, Mancini responded by removing Silva for De Jong in an effort to exert more presence in the centre of midfield. Wolves made their own change as striker Kevin Doyle came on for midfielder David Edwards, signifying a change in priorities for both sides.
Mancini's frustration grew on the sidelines as, deprived of the talented Silva, who was disappointed to be removed, City struggled to replicate the slick passing of their first-half performance and were drawn into an entrenched battle at Molineux.
However, with dark clouds encircling Molineux, the growing gloom lifted on 74 minutes as Nasri added a second. Tevez won and then took a quick free kick and after exchanging passes with Toure released Nasri with a fine pass across the face of goal. With Bassong having pulled up with a hamstring injury that later forced his withdrawal, the Frenchman had the time to control and then dispatch a fine low drive past De Vries.
The goal gave City the cushion they craved and Mancini's side could have extended their lead as substitute Adam Johnson went close and Stearman almost put a header into his own net in the closing stages.
However, 2-0 was sufficient to ensure that all eyes are now firmly trained on the Manchester derby on April 30 which could decide the destination of the Premier League title.