This hard-fought win left lingering uncertainty over just how good Pep Guardiola’s Manchester City are. There was little of the carousel pass-and-move play the Catalan yearns for and though victory is the bottom line, no hard evidence exists his side will secure a Champions League place for next season, never mind the title.

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With Ilkay Gündogan out for the rest of the season due to injury, Guardiola could ill-afford to lose another midfielder. Yet off went Fernandinho in the first half for a second Premier League red card (and third in all) to rule him out for four games, thus taking City’s tally to seven dismissals this season. Guardiola was decidedly upset and in his subsequent refusal to accept the side have a disciplinary problem indicated he is feeling the strain.

City were gifted the ideal moment to blow away the blues from their defeat at Liverpool during the first exchanges. A careless pass from Ben Mee ceded possession and Kelechi Iheanacho was through on Tom Heaton. The goalkeeper showed his quality as he smothered the Nigerian’s shot and when the ball diverted to Yaya Touré he might have attempted a shot himself. Instead, he found Raheem Sterling and when the forward let fly Heaton once more saved Burnley.

Seconds later Touré easily turned the away defence and slipped in Iheanacho but after the forward dallied, Michael Keane made a block.

Kevin De Bruyne disappointed by firing the subsequent corner straight at George Boyd and this became the tale of City’s afternoon: a series of let-downs near Burnley’s goal. When Sterling led a breakaway following a rare Burnley corner his pace took him into opposition territory. Yet after the ball went to Jesús Navas the Spaniard’s left-foot cross lacked conviction.

Navas was one of four changes Guardiola made for the match – he dropped David Silva, John Stones, Sergio Agüero and Pablo Zabaleta and in came Iheanacho, Bacary Sagna and Gaël Clichy.

Fernandinho’s sending off came in the 32nd minute after he tackled Johann Berg Gudmundsson with both feet raised. It appeared the correct decision and from this point City became more ragged and the first half ended with Aleksandar Kolarov, De Bruyne and Sterling all having been outmuscled. Only Touré had been an asset against a Burnley team that offered scant threat.

Guardiola may have had a few choice words for his players during the half-time interval. He also appeared to admit his error in selecting Navas and Iheanacho as on came Silva and Agüero. The manager had also implored the City crowd to make more noise but after a brief increase in volume they became as becalmed as their team.

If the idea of introducing Silva was to increase the tempo there was an early sign it might work. His interplay with the under-par De Bruyne led to the ball being under Agüero’s feet in the area but Stephen Ward cleared. But then came the opener: Sagna floated in a ball from the right and it went all the way across the area to Clichy. After a shimmy the left-back let go with his right boot and scored only the third goal of his City career.

Four minutes later the lead was doubled. De Bruyne raced forward and delivered his best pass of the match, to Sterling, who received and advanced on Heaton. But the forward fell over, which allowed the goalkeeper to stab at the ball only for it to fall to Agüero and his shot pinballed off a post and Matthew Lowton’s arm into the net to make it 2-0. It took Agüero to 17 for the season and to third on the all-time list for the club, equal with Colin Bell’s 153 goals.

At this point City should have coasted but instead Burnley pulled one back. Claudio Bravo flapped at a corner and from the ensuing melee Mee forced the ball home – marginally, goal-line technology showed. City were not happy and surrounded the referee, Lee Mason, and assistant referee Ian Hussin, which led to a yellow card for Sagna.

The home side just about clung on – Keane went close at the death – and Guardiola must be concerned at precisely where they go from here.

The Burnley manager, Sean Dyche, said: “Bravo? I’ve seen it back, I think it’s just a goal. Two honest challenges, it drops then goes in. Just part of the game. I actually thought we did better 11-v-11. The way we shut them down from playing out was very good.”

City are on 42 points, seven behind the leaders, Chelsea, who also have a game in hand. Cue more irritability from Guardiola regarding their title prospects. “Yesterday, no,” he replied. “Why are we in the title race today?”