The Ivorian scored a goal in each half against a Palace side who markedly improved after the break, levelling midway through the second period.
If the Ivorian had dreamed of the perfect comeback, this was surely something close to it as the Blues left Selhurst Park with a much-needed 2-1 win.
The first-half hour was largely devoid of incident with neither side making the opposition goalkeeper work too hard.
City looked comfortable in possession without threatening while Palace struggled to make any inroads at all.
The first real opportunity came on 18 minutes when Nolito where the Spaniard had the ball whipped off his toes.
Then Nolito played a smart ball in behind the Palace defence for Aleksandar Kolarov to whip a ball into the six-yard box but Sergio Aguero was caught in two minds and his effort looped up and wide.
The luckless Vincent Kompany, recalled along with Yaya Toure, Bacary Sagna and Nolito, was clattered in a collision with Claudio Bravo just past the half-hour mark and the severity of his fall to the ground suggested his jinx may have struck again.
Kompany played on for a few minutes before blurred vision meant he could no longer continue – on the plus side it’s an issue that will not keep him sidelined for too long but the Belgian defender must wonder when his fortunes will change.
Two minutes later and City finally broke the deadlock with a goal that smacked of quality.
Sterling forced an error from Kelly just outside the Palace box, Kevin De Bruyne picked up the loose ball and fed Yaya Toure.
The Ivorian’s initial pass to Aguero forced the Argentine wide - but he returned the pass to Toure who, with nothing obvious on, spotted Nolito, played a quick one-two before rifling a shot past Wayne Hennessey.
The shot took a meaty deflection from Scott Dann, but nobody was complaining as the returning midfielder reminded everybody of his explosive talent.
The Blues continued to boss the game in the opening stages of the second period, but the hosts came close to levelling just before the hour-mark when Jason Puncheon wriggled his way to the bye-line before picking out the head of Christian Benteke who seemed certain to score, but his effort was well saved by Bravo and the rebound fired wide by Wilfried Zaha.
Moments later and Benteke went close with another header – the warnings had been well and truly posted.
The game swivelled on its axis within the space of 30 seconds on 65 minutes when City counter-attacked with menace and De Bruyne’s cross found Aguero whose delicate flick was scrambled off the line by Joel Ward.
From the clearance Palace surged forward and when the ball found Connor Wickham who lashed a left-foot shot past Bravo to level the scores.
It had been coming.
City, however, weren’t prepared to see another two points go begging and shifted up a gear, pressing Palace back in their own half looking for the winning goal and on 82 minutes, the Blues again took the lead.
De Bruyne’s low corner found its way into the six yard box and – who else? - Yaya Toure was on hand to calmly guide home his second of the game and wrap up a precious three points.
Moment of the match
Joel Ward’s clearance as Sterling looked set to turn home the shot Aguero had come so close to turning home proved vital for Palace who were level within seconds – such are the margins between success and failure – though Yaya would have the final word with his second of the afternoon.
Picture of the match
Man of the match: Yaya Toure
Calm in possession with his array of passes the usual mix of incisive and simple, Yaya was at times back to his very best – not bad considering he hasn’t played for so long.
His first goal was typical Yaya Toure and his second was calmness personified.
On this evidence he will have given Pep Guardiola a very welcome headache – welcome back, big man.
City travel to Germany to face a Borussia Monchengladbach side knowing that defeat will mean the Blues will progress to the knock-out stages of the Champions League.
Expect John Stones and Ilkay Gundogan to return, though Yaya Toure is ineligible.