The Blues lost skipper Fernandinho on 32 minutes but fought back to score twice after the break in a hotly-contested affair.
Former City defender Ben Mee pulled a goal back for Burnley but the Blues hung on for deserved three points.
City started the day needing to get back to winning ways after the New Year’s Eve loss to Liverpool.
The first chance was the better of the two, as Raheem Sterling slipped him clear only for keeper Tom Heaton to block his effort and then poke the ball of Sterling in the melee that followed.
The young Nigerian then curled a deflected shot over a couple of minutes later as the Blues looked to get an early foothold that has sometimes evaded them in a number of home games this season
Another lightening Sterling break on 17 minutes gave Yaya Toure forced Heaton into another decent save with a shot from 20 yards.
Well organised and determined, Burnley were frustrating the hosts and just past the half-hour mark City’s task became that much harder when Fernandinho was shown a straight red for a full-blooded tackle on Gudmundsson.
Down to ten men with two thirds of the game left, the Blues looked up against it and Guardiola decided to bring on David Silva and Sergio Aguero at the break in an attempt to shake things up.
City continued to press despite being a man down, but with greater purpose and menace and on 58 minutes were rewarded with a goal – something of a collectors’ item – as Gael Clichy cut in from the left before striking a low shot past Heaton.
Four minutes later and the Blues had doubled the lead. De Bruyne’s through-ball to Sterling looked a yard short, but the England winger managed to take the pass in his stride, trip as he attempted to round Heaton and Aguero powered the loose ball home from a tight angle and despite there being two defenders on the line.
It was just reward for the Blues who, far from going into a defensive mindset following Fernandinho’s sending off, shifted up a gear.
The game was far from over, however and on 70 minutes and almighty scramble in the City box ended with former youth team skipper Ben Mee forcing the ball over the line.
There were one or two nervy moments in the time that remained of an increasingly ill-tempered affair, but anything other than a victory would have been harsh on City given the circumstances.
Key moment: Ferna dismissal
City were plugging away without success, but comfortable and in control when Fernandinho’s pass to De Bruyne was intercepted by Johann Berg Gudmundsson. In an effort to win possession back, the Blues’ skipper energetically slid in on the Icelandic midfielder who went down clutching his leg.
There will be arguments for and against Lee Mason’s decision to brandish a straight red card but it matters little as the Brazilian was sent for an early bath regardless - but instead of hurting the Blues, it seemed to galvanise the home side into life and undoubtedly change the course of the game.
Star man: Kevin De Bruyne
Tireless running by the Belgian from start to finish, he was the beating heart of City team and his energy and verve helped turn around what could have been a difficult 90 minutes.
What it means…
The Blues climb back into third spot but are now only two points adrift of Liverpool who surprisingly drew 2-2 at Sunderland – at least for 24 hours with Arsenal and Spurs in action tomorrow.
Liverpool’s point keeps them second with Chelsea away to Tottenham on Tuesday evening – for now, the gap to the leaders is back to seven points.
Photo of the match
A break from Premier League action now for City who travel to the London Stadium for the first time this Friday to take on West Ham United in the FA Cup Third Round.