Manchester City 3 West Brom 1

There is a song that can be heard on nights like these at Manchester City and it takes its tune to the words “we’ll fight to the end”. They were true to its theme two seasons ago – right to the very last kick of the season and that throaty commentary of Sergio Aguero’s moment – and now they are clinging to the hope that something similar might be possible again.

They will almost certainly need Chelsea to win at Anfield on Sunday against a Liverpool side that have won 11 games on the bounce and it would be stretching the truth to say there was any real sense here that City's crowd might be witnessing another spectacular comeback in the making. For now, however, they are doing their bit, seeing off West Brom with first-half goals from their Argentinian contingent and emerging unscathed from a more prosaic second half apart from losing David Silva to injury.

Pablo Zabaleta and Sergio Aguero both scored inside the opening 10 minutes and, at that stage, it was tempting to wonder whether West Bromwich might be on the receiving end of one of the thrashings that were regularly handed out here earlier in the season.

As it turned out, Graham Dorrans briefly gave the Premier League's 16th-placed side hope with a fine counterattacking goal after 16 minutes. Martín Demichelis soothed any gathering nerves from a corner and it was probably a surprise that the scoring stopped there.

In the process, Manuel Pellegrini’s side have moved to 145 goals in all competitions this season. It is a new record for a top-division team, the previous high having been set by Matt Busby’s Manchester United, with 143 in 1957.

West Brom were obliging opponents on that front but Silva’s return from injury was also pivotal and it will be a considerable setback if this was his last contribution to the season.

If there was a downside, it was that City have now gone five games without managing a clean sheet. Dorrans took his goal with great expertise, deceiving Gaël Clichy with a clever change of direction and elegantly sweeping the ball past Joe Hart. Yet it will not have escaped Pellegrini's notice that all this originated from a poor free-kick routine in the opposition half. Liam Ridgewell dispossessed Pablo Zabaleta and it was remarkable how vulnerable City suddenly were as Stéphane Sessegnon and Matej Vydra led the counterattack.

The problem for Pepe Mel’s side was that, against this calibre of opponent, it is reckless to defend this generously and expect to get away with it. The opening goal, after three minutes, was the case in point, starting with Ridgwell’s poor defensive header straight to Agüero.

The former England goalkeeper Ben Foster saved the striker's shot but Zabaleta was following in and Chris Brunt had not tracked the full-back's run. Zabaleta's stooping header made him the 14th different scorer for City this season.

Agüero’s finish to make it 2-0 was a beauty, clever enough to realise that Foster was badly positioned and benefiting from Morgan Amalfitano’s failure to clear properly. Foster had taken a step too many to the right, leaving an inviting gap for Aguero to pick out on the goalkeeper’s left, and it was that kind of basic mistake that was West Brom’s undoing.

Demichelis's goal originated from nothing more elaborate than the classic flick-on and far-post corner routine. Samir Nasri swung the ball over and Vincent Kompany applied the first touch before Demichelis arrived from behind to restore the home team's two-goal advantage.

Albion moved the ball nicely at times, with Dorrans continuing to impress, but without really giving the impression that they could do a great deal more to invigorate the small corner of visiting supporters. Sessegnon’s direct running sporadically caused problems and a moment of erratic handling from Hart earlier in the match might also have encouraged them.

For the most part, however, it was a relatively stress-free second half for City bar that moment, after 68 minutes, when Silva went down in obvious pain by the right touchline. The challenge with Amalfitano had looked fairly innocuous but Silva has been troubled with an ankle injury for some time. This was his return to the team after missing the 2-2 draw against Sunderland last week and his performance had re-iterated his importance to the team. He can only hope that the injury is not too serious and he will be back to help City in their bid to catch Liverpool at the top.

By that stage, City were simply going through the motions. Albion had seldom shown the ambition to believe they could emulate what Sunderland had managed when they won at Chelsea on Saturday. They, too, lost a player through injury, with Ridgewell hurt in a challenge with Zabaleta, and the defeat leaves them hovering three points above the relegation zone, albeit having played a game fewer than three of the four teams directly beneath them.

Demichelis finally took the game’s man-of-the-match award and City, needing to win all their remaining four games, must now hope the news on Silva is not too bleak.