It was the night Carlos Tevez was reintroduced to the Premier League but, for Manchester City, they will cherish what happened here for different reasons. Tevez's first appearance since September was only a sideshow compared to the real story of what this victory means for Roberto Mancini's team, the consequences at the top of the table and the message it sends to Manchester United.

This was the night they set a new Premier League record of 20 straight home wins but, of far greater importance, it was also the moment when they made it very clear they are not just going to crumple now the advantage is with the team from Old Trafford.

Alan Hansen had talked of this team being on the brink of "capitulation" after their defeat at Swansea and yet here they were, recovering from a goal down, showing the resolve and strength of personality that any team with genuine championship credentials needs.

They had gone behind after an hour, via Gary Cahill's deflected shot, to a Chelsea side that has rediscovered the art of winning football matches and, briefly, there was the inescapable sense of a telling, potentially devastating blow, to their title hopes.

Instead, what followed was a demonstration of the qualities that Mancini has been trying to cultivate. City kept pressing forward, Tevez was brought on for his energy and drive and, in the end, they wore Chelsea down. Sergio Agüero equalised with a 78th-minute penalty and then there was the final, frenzied onslaught of the Chelsea goal that eventually saw Samir Nasri poke in the goal which means City have clambered within a point of United.

Almost inevitably, Tevez was involved in the game's decisive moment. There were boos when he was introduced, but plenty of applause, too. Many supporters are clearly willing to overlook his transgressions if he can be of use between now and the end of the season. Here was his first contribution. With five minutes to go, Nasri exchanged passes with the Argentinian, carried on running and slipped his shot past Petr Cech.

Mancini's victory jig on the touchline encapsulated the emotions of the night. Afterwards, true to form, City's manager was not entirely satisfied.

Invited to praise Nasri, he chose instead to say the Frenchman "could do better". There was criticism of Balotelli – "I didn't like how he played" – and he admitted the team "had not played well for three or weeks". But there was relief, too. The fixture list is so obliging to Sir Alex Ferguson's team over the coming weeks that City simply had to win this match.

Mancini even borrowed the famous Ferguson line. "It felt like squeaky-bum time," he smiled.

For long spells the quality was low, from both sides. City, however, probably deserved to win on the balance of play and their sheer perseverance. Nasri was the most creative player on the pitch, hitting the crossbar with a first-half shot, and Yaya Touré was a key figure, driving forward from midfield.

Yet there were moments of carelessness, too. David Silva's usual accuracy with his passing had deserted him. Agüero looks like he is feeling the effects of a long, sapping season and Balotelli did not even make it beyond half-time. The Italian had run clear, courtesy of a horribly misplaced pass from Frank Lampard after 29 minutes, but dragged his shot wide and was scarcely involved otherwise.

Chelsea, too, looked weary, lacking structure, misplacing far too many passes, particularly Ramires and Raul Meireles. At times Fernando Torres looked sharper, in short bursts, than we have seen him for the most part this season. At other moments he reverted to being isolated, lacking the old sureness of touch, culminating in his scowling substitution.

City were missing both their first-choice centre-backs, Vincent Kompany and Joleon Lescott, and could feasibly have been more vulnerable had Didier Drogba started.

Chelsea's goal came from their first shot on target. It originated from a corner and, as City struggled to clear their lines, they felt the referee, Mike Dean, should have stopped the play, first when Torres gave Touré a little nudge and then when David Luiz did similar alongside Gareth Barry, Balotelli's replacement. City had defended the corner poorly and when Cahill swung his right foot at the ball the ricochet off Touré was against them.

Mancini reacted by bringing on Tevez but it was City's other Argentinians who combined for the equaliser, Pablo Zabaleta's shot striking the substitute Michael Essien's left arm and Agüero scoring, emphatically, from the penalty spot.

The stage was set for one final flourish and, between them, Tevez and Nasri reminded United how difficult it is going to be to shake off the team hanging on their shoulder.