If Manchester City are supposed to be concentrating their resources on returning to the top of the Premier League after securing European football for next year, they went an odd way about it, resting John Stones and Ilkay Gündogan and leaving David Silva and Kevin De Bruyne on the bench. Crucially, they did not omit Sergio Agüero, and two of the striker’s scruffier goals were enough for City to take the points after going behind.

“They were beautiful goals,” a beaming Pep Guardiola insisted. Sean Dyche was closer to the truth with “two blips in a really good gameplan”, but though Burnley might have had a first-half penalty when Nicolás Otamendi barged into Jeff Hendrick, the home side had to accept they did not do quite enough to knock City out of their stride.

Burnley 1-2 Manchester City: Premier League – as it happened Read more

The visitors must have been encouraged by the knowledge that a calf injury had ruled out Tom Heaton, something of a lucky talisman for Burnley this season, at least the way José Mourinho tells it. The home fans were not exactly thrilled at the news that 37-year-old Paul Robinson would be making his Burnley debut after two years without a league game – though, in the event, the former England goalkeeper took up where Heaton had left off, making a couple of first-half saves from Agüero that prevented his side conceding first.

Better than that, it was Robinson who provided an assist when City conceded first. Burnley sent everyone forward for a free-kick that the keeper clipped into the goalmouth and Dean Marney pounced gratefully on a half clearance to score with a right-foot volley from the edge of the area.

If City needed a wake-up call – and a generally flat first-half display suggested that they did – Marney did well to provide it before being forced off with an injury. Burnley’s only worry, apart from the fact that Johann Gudmundsson also pulled a hamstring and followed Marney down the tunnel before half-time, was that City still had more than an hour to get their act together and respond.

It took them a while; this was far from their slick and smooth-passing best, but shortly after Yaya Touré had struck the frame of the goal and booted the ball away in frustration, Raheem Sterling and Nolito forced Michael Keane to concede a corner and with the ball bobbling untidily around the six-yard box Agüero poked home a close-range equaliser.

Goal of the season contender it was not, but Agüero was back in more recognisable form before the interval in bringing a fingertip save from Robinson with a curling shot.

City might have taken the lead in the four minutes of first-half stoppage time occasioned by the two Burnley injuries, but though Sterling and Agüero could virtually have passed the ball into the net, they were far too casual in finding each other and the opportunity was missed.

The visitors kept up the pressure in the second half, forcing Burnley ever deeper in defence, and the only surprise when Agüero gave the visitors the lead on the hour was that, again, Robinson was beaten from just a couple of yards out. A move appeared to have broken down when Touré was upended in the box after a surging run, but rather than pressing claims for a penalty, Fernandinho chased down the ball to cross from the narrowest of angles and Agüero made sure he was in place to supply the required touch.

Facebook Twitter Pinterest Agüero watches as his touch sends the ball over the line to score. Photograph: Matt West/BPI/Rex/Shutterstock

The Argentina striker found himself on the wrong side of the referee soon afterwards for chipping the ball into the net after being ruled offside. One could understand Agüero’s annoyance: he seemed to be at least level with Stephen Ward, though the consequences are clear for anyone expressing displeasure in such a manner.

The match became a little fractious in the final quarter, with Nolito cautioned for bumping into Scott Arfield and then being withdrawn before he did anything more serious. While it is true that Nolito appeared in danger of losing his temper, the alleged foul on Arfield was nothing compared to the high challenge George Boyd got away with on Bacary Sagna moments later.

Burnley had their moments as they tried to salvage a point, most notably in stoppage time, when Claudio Bravo saved from Ashley Barnes and Keane almost got his head to a cross that the goalkeeper fumbled, but City toughed out their win in a manner that pleased Guardiola.

Fielding questions in Spanish about the feistiness of the smaller clubs in the Premier League the City manager was highly complimentary about Burnley. “They do what they do very well,” he said. “It is very rewarding to win here as well as at Stoke City.”