Roberto Mancini's side started slowly but ruthlessly hit four second half goals to keep pace with rivals Manchester United at the top of the Premier League.
Not even an injury to striker Sergio Aguero could undermine a result which will help City recover from a week which saw Tevez's two-year spell at Eastlands reach a sorry end in all but name.
City made six changes from the team that surrendered all too easily against Bayern Munich at the Allianz Arena on Wednesday night.
And after showing they had much to learn at Champions League level, they set about trying to stay on the coat-tails of Manchester United.
Their best chance of the half fell to Mario Balotelli, who after receiving James Milner's pass from the byline, somehow blazed over from 12 yards.
Mancini's difficult week got even worse in the 27th minute when Aguero left the field having been limping for the previous five minutes and was replaced by Samir Nasri.
The Argentine looked to be struggling with his groin and his absence, along with that of Tevez, will give Mancini a further headache with his team selection.
After a lifeless display before the break, the Italian will no doubt have reminded them of the opportunity they had to take a precious three points against Steve Kean's Rovers side which had won just once all season.
In the opening moments of the second period, David Silva carved an opportunity which allowed him to send a shot with the outside of his boot just inches wide of Robinson's goal.
Then in the 50th minute City upped the ante again when Balotelli drifted into the box, worked another opening and this time curled a superb strike beyond Robinson and against the upright before the ball bounced away to safety.
Six minutes later, last season's FA Cup winners finally edged ahead. A corner by Aleksander Kolarov was headed away by Rovers defender Gael Givet.
The ball landed only as far as Adam Johnson, who steadied himself before curling the ball into the top left hand corner of the net with his favoured left foot.
It was a mighty relief for City, and Johnson's moment of inspiration provided them with the impetus to add a second just three minutes later.
Nasri, who had been bright since replacing Aguero, found space on the left and whipped in a cross which Balotelli expertly flicked past Robinson at the near post after meeting the ball ahead of Steven Nzonzi.
That looked to have settled the contest and appeared to provide the perfect backdrop for a section of the home support to stage a planned sit-in demonstration in protest at the way Kean is managing the team.
But there was more to come from City in the 73rd minute when Silva launched a counter-attack and found Nasri on the left.
The former Arsenal playmaker cut inside and laid the ball off to James Milner. His shot rebounded off a defender and into the path of Nasri, who fired a deflected shot past Robinson for his side's third.
The third goal brought out the anger in the home crowd. The deafening chants of "Kean out" and "You don't know what you're doing" could no longer be dismissed as a tiny minority hoping for the removal of their manager.
As for City, the class that a transfer spend in excess of £300m buys you meant they were not quite finished. Another corner from the left by Kolarov was met powerfully by the head of substitute Stefan Savic, who had been on the pitch for just eight minutes.
That was the cue for thousands more Rovers fans to head for the exit after seeing their team mercilessly torn apart by Mancini's expensively-assembled team.
Source: AFP
Source: AFP