Welcome to Manchester. That was the slogan on the notorious billboard which greeted Carlos Tevez's move from United to City and on Wednesday night the blue half of Manchester welcomed him all over again, the £30,000-a-day prodigal son.

Looking a little tubbier after his unscheduled six-month holiday, the man Roberto Mancini declared would never wear the club's shirt again was on the pitch for just under half an hour against Chelsea and made a significant contribution to both their goals. Without him, City looked haphazard and demoralised. With him, they reacquired a sense of menace and the look of championship challengers. As simple as that.

It is dangerous to make even a reasonable assumption about what goes on inside Tevez's head, but the Argentinian forward may have been pleasantly surprised by the reception he received from City's fans, many of whom have spent the last few months recasting him from hero to traitor.

Stepping out of the team coach, he was given a bigger cheer than any of his team-mates and responded with a grin and a genial thumbs-up. By the end of the night he would have the applause of 40,000 ringing in his ears.

There were a few discreet boos amid the ripple of applause inside the stadium when his face first appeared on the big screens while the team announcements were being made. He was included among the substitutes for the first time since that September night in Munich when he committed what some of us regarded as a crime against football by refusing Mancini's instruction to warm up in preparation for an appearance during the second half, with his team-mates two goals down and desperately in need of assistance.

Many remain scandalised by his behaviour on that occasion, a gesture seemingly consistent with a nomad's attitude to loyalty while being strangely at odds with the wholehearted commitment he has always shown when involved in the actual business of trying to win or to save a match. And which, when he was eventually given the chance, he demonstrated again last night.

The pre-match reaction to Tevez's possible return offered a clear view of the changed relationships within today's football. In the old days, the constituent elements of a club – its directors, its players, its supporters – shared a common cause. The arrival of billionaire super-owners introduced a division between a club as embodied by its supporters and its history on the one hand, and its owners and its coaching and playing staff on the other. What they have in common is a desire for success, but their underlying purposes are different and they may have different views on how that success should be achieved.

Tevez's return to action owed everything to the cold-blooded pragmatism of the modern world. As City lost momentum at exactly the time when they should have been re-emphasising the seriousness of their challenge, the cost of Tevez's absence became starkly apparent. The clarity and incisiveness of their play disappeared along with the points that provided a cushion over Manchester United.

Their plight was all too apparent in the first hour against Chelsea, provoking noises of exasperation as corner-kicks failed to clear the first defender, passes short and long went astray and Mario Balotelli made a mess of the best chance of the half when he rolled the ball wide of the post after Frank Lampard had mystifyingly sent a square pass straight to his feet just inside the Chelsea half, inviting him to outpace the defenders and bear down on Petr Cech. At that very moment Tevez was starting his first warm up on the touchline, to another burst of applause that seemed to express the fans' desire to see someone in a blue shirt capable of giving them at least a glimpse of directness and decisiveness.

Ten minutes into the second half, Mancini again beckoned Tevez to warm up. He was jogging up and down when Chelsea took the lead, and was immediately summoned to get ready for action. And in the 66th minute, when Nasri let a pass run under his foot and into touch, there he was, on the pitch again, once more playing an active part in the great soap opera of the Premier League.

In the 77th minute he lost possession to José Bosingwa and then, with characteristic tenacity, regained it before slipping a pass through to Edin Dzeko. The Bosnian's shot was deflected, providing the corner that led to the handball which led to Agüero's penalty. Eight minutes later Tevez's deftly smuggled return pass to Nasri permitted the Frenchman to supply City's winner.

Had Tevez made the difference? You bet he had, and not for the first time. Or, you might imagine, the last.