It was Sean Dyche's side that took a shock lead, with Dean Marney's 14th-minute effort, City had some decent efforts before Aguero's equaliser in the 37th minute. The three points were secured on the hour mark, with the Argentine's second of the afternoon. Burnley went close early on, with efforts from Michael Keane, but City held out.
City came to Turf Moor after securing their last-16 place in the Champions League with their 1-1 draw with Borussia Mochengladbach. They got their eye in the eighth minute, testing veteran goalkeeper Paul Robinson, but they managed to find themselves behind in some spectacular style in the 14th minute.
Robinson hoofed the ball down field, which looked to be cleared by Nicolas Otamendi. It was perfect for Marney who hit the effort on the volley, past Claudio Bravo and into the bottom corner.
Starting to get into it
That opener seemed to kick Guardiola's side into gear, and had some decent efforts to get themselves back in the game. The first came in the 21st minute, as Nolito opened his body to try and find the bottom corner, but Robinson was there to get down well and save.
Their best opportunity came ten minutes from the break, it came from Yaya Toure who had a great resurgence after last week's performance against Crystal Palace. The Ivorian looked to continue his good form, as he looked for the near post from the right-hand side of the area but it clattered the woodwork.
Got one back
Their close opportunity seemed to ignite City even further, and they found themselves back in the contest just two minutes after Toure's opportunity. It was a scrappy effort from City, as the flicked-on corner was poorly cleared, and it was Aguero who was alive to the situation as he stuck it under Robinson.
He could have easily made it two in the 39th minute, the Argentine came in from the left and let rip, and it looked destined for the corner but Robinson did brilliantly to get down and steer it wide.
It was quite a slow start to the second period, but it burst into life on the hour mark as City managed to nudge themselves ahead. It was once again very poor from the Clarets, as they failed to clear the ball. It eventually fell to Fernandinho, and the stand-in skipper's cross was turned home by Aguero.
However after taking the lead, City took the pedal off the gas and Burnley reacted with two decent opportunities to get themselves back into the contest. The first came in the 75th minute, when the ball was played into the back post towards James Tarkowski, City failed to deal with the second ball as he headed towards Keane but the effort was eventually blocked.
As the match came towards the end of stoppage time, Burnley almost had the golden opportunity to equalise, Bravo failed to claim the high ball and it fell to Keane. City were once again slow to respond, but unluckily for the former Manchester United defender, it came off the back of Ben Mee, and City managed to hold out.