Ten-man Manchester City moved up to third as they withstood a spirited Burnley fightback in front of a relieved Etihad Stadium.
Fernandinho was dismissed towards the end of an even first half for a two-footed challenge on Johan Gudmundsson.
But the hosts improved after the break as Gael Clichy squeezed home a shot before Sergio Aguero, on as a substitute, fired home from a tight angle.
Ben Mee smashed home via the underside of the bar shortly after but Burnley could not force a leveller despite a fine chance for Andre Gray late on.
City take the hard road
Beginning the day 10 points behind leaders Chelsea, anything less than victory would have prompted some to begin reading the last rites on City’s title challenge.
As it is, Pep Guardiola’s side will look at the league table with renewed optimism as they closed to within two points of second-place Liverpool with one and possibly both of Chelsea and Tottenham to drop points when they face each other on Wednesday.
However, Fernandinho’s dismissal meant they had to fight harder than they might have expected for victory.
The City captain took some of the ball as he contested a 50:50 ball in midfield, but his reckless scissor-action style meant that referee Lee Mason’s decision to show red could be easily justified.
It is not the first time City’s discipline has hindered their title ambitions. Including Sergio Aguero’s retrospective red against West Ham, they have been shown seven red cards in Guardiola’s 30 games in charge.
Fernandinho’s third red card in six games for City means he will be banned for four matches and not available again until 5 February.
Aguero off the bench and to the rescue
Well before Fenandinho’s lunging challenge, Guardiola’s team selection seemed to have hampered rather than helped City’s cause.
Aguero, who was spared the rigours of the festive fixture list after only making his comeback from a four-match ban in the New Year’s Eve defeat by Liverpool, was left on the bench with Kelechi Iheanacho preferred up front.
Iheanacho missed the best of what little City created in the first half and Aguero brought a more threatening edge to the hosts’ attack when he was introduced alongside David Silva at half-time.
The Argentine’s dead-eyed finish from a tight angle, past two covering defenders, provided the winner and convincing evidence for an immediate recall.
Burnley come close on return to Manchester
Burnley have only won a single point away from Turf Moor this season, but they can count themselves unlucky not to follow their October draw at Old Trafford with similar on their return to Manchester.
While they confounded United with a stubborn rearguard action, Sean Dyche’s side went toe-to-toe with City even before Fernandinho’s red card gave them an extra man.
Mee’s goal, awarded with help by the decision review system, exposed goalkeeper Claudio Bravo’s uncertainty in the air, but Burnley created enough to take a point without City’s errors.
The precision that Gray showed in scoring his hat-trick against Middlesbrough last time out deserted him in injury-time while Sam Vokes glanced just wide when well placed.
The Clarets remain 11th, eight points above the drop and well above par for the season so far.