Pep Guardiola's Premier League leaders were bitterly disappointing in the first-half at the Etihad Stadium and Ashley Barnes profited from a John Stones mistake to put the Clarets ahead. The hosts were much-improved in the second-half though, and two goals in three minutes from Sergio Agüero turned the tie on its head.
Leroy Sané struck mid-way through the second-half with a low finish before setting up Bernardo Silva for the fourth as City sailed through to the next round.
Both managers made four changes apiece as their respective FA Cup campaigns kicked off at the Etihad Stadium. Manchester City boss Pep Guardiola introduced the likes of Oleksandr Zinchenko, Ilkay Gündogan and Danilo for Fabian Delph, Kevin De Bruyne and Kyle Walker respectively. Claudio Bravo meanwhile started in goal in place of Ederson.
The injured Scott Arfield dropped out of the Burnley team for striker Ashley Barnes. The forward was also joined by the likes of Matthew Lowton, Kevin Long and Ashley Westwood.
Stones slip-up gives Burnley shock lead
In typical 'City' fashion, the home side created numerous opportunities straight from the off. Sergio Agüero did well to wriggle towards the by-line and cut the ball back only to see the cross take a touch off of Charlie Taylor and deflect towards goal but Burnley cleared. Leroy Sané found space in the penalty are but could only put his shot well wide.
Former Manchester City defender, Ben Mee, then had a fantastic opportunity for Burnley. His towering header from a corner bobbled along the face of goal before the Sky Blues managed to scramble clear.
The opening goal arrived soon after and it was current City centre-back John Stones who played a key role. The Englishman looked to be performing a routine clearance, only to see the ball skid off of his shin and straight into the path of Ashley Barnes. The striker tore down on goal and thundered into the near post past Claudio Bravo to give the Clarets a shock lead.
Quick-fire Agüero double puts City in control
In what was a frustrating half for Pep Guardiola's men, their only real chances of note were from distance. First, Oleksander Zinchenko twice fired over from the edge of the area before Fernandinho followed suit and sent a powerful effort whistling just over the cross-bar.
The hosts were far more dynamic in the second-half and it only took them 11 minutes to get level. İlkay Gündoğan played a quick free-kick to Sergio Agüero who was unmarked in the penalty area. The Argentine then sped through and finished low past Pope.
The 29-year-old then notched another barely two minutes later. Combining well with Gündoğan again, the duo played a quick one-two. A back-heel from the German midfielder put Agüero through and he slid the ball under Pope to complete a fantastic turnaround and notch his 16th FA Cup goal in as many appearances.
Sané could well have applied gloss to the result but somehow skied his shot only yards out.
Sané secures progression for Guardiola's men
The German international did eventually get the third goal however. Speeding in from the right, the former Schalke 04 wide-man prodded underneath Pope and into the net to cap a lively performance.
Substitute Bernardo Silva also got in on the act following a lung-busting break. Sané skipped around the advancing goalkeeper and squared the ball to the former Monaco man who duly slotted into the empty net and made sure there was little doubt of City's ticket in the Fourth Round draw.