The victory takes Pep Guardiola’s side, into provisional second spot and back within eight points of leaders Liverpool.
Manchester City's Gabriel Jesus struck twice and Rodri scored a screamer in a 4-1 win at Burnley on Tuesday as the champions showed signs they may be able to keep the Premier League title race alive.
The victory takes Pep Guardiola's side, who had drawn at Newcastle United on Saturday, into provisional second spot and back within eight points of leaders Liverpool ahead of the Merseyside derby with Everton at Anfield on Wednesday.
Jesus opened the scoring in the 24th minute and doubled City's advantage five minutes after the break before a spectacular drive from Rodri and a low drilled shot from substitute Riyad Mahrez made it four.
A late consolation from Burnley substitute Robbie Brady will have annoyed Guardiola, whose side have now gone eight games in all competitions without a clean sheet but, that aside, this was back to business for City.
The Spaniard, though, dismissed talk of a title race comeback.
"For the distance we have with Liverpool it would be crazy to think about the title, we have to think about the (weekend Manchester) derby, the other competitions, and take this rhythm," he told the post-match news conference.
The way the City players celebrated the win showed they knew they could ill-afford another slip-up after being held at Newcastle United on Saturday.
In recent weeks City have looked well below the standards set in their two straight title campaigns and this season they had already dropped 13 points in their 14 games, only three short of their total for the whole of the last campaign.
With only one win in their last five games in all competitions, the pressure on City was real but the gap in quality between the elite clubs and the tightly-packed middle ranks of the Premier League was soon evident.
Burnley manager Sean Dyche switched from his usual 4-4-2 to a five-man midfield with Danny Drinkwater, on loan from Chelsea, making his first Premier League appearance in 21 months, but neither he nor his team mates troubled the champions.
City began to move the ball around with the kind of confidence and precision that has been their hallmark under Guardiola and they were soon ahead.
The breakthrough came after a swift exchange of passes ended with David Silva threading the ball to Jesus who, filling in for the injured Sergio Aguero, curled a shot into the far corner.
The lead could have been doubled two minutes before the interval when, after rare Burnley pressure, City broke and the counter ended with a Bernardo Silva drive which keeper Nick Pope saved superbly with his outstretched leg.
The second goal came when Bernardo Silva curled a probing cross towards the back post and Jesus reacted quickly to get in front of his marker Phil Bardsley and volley home.
Jesus, who had not scored in his previous 10 games for club or country, was buzzing and went close to a third with a burst of pace and another shot that fizzed just wide of the far post.
A blocked shot from David Silva then fell to Rodri on the edge of the box and the Spaniard blasted a thundering, unstoppable drive past Pope to make it three in the 68th minute.
Mahrez, given acres of space, got the fourth goal three minutes from the end with a low shot from the edge of the box before Brady gave the muted home crowd some cheer in the cold.
"We played with an incredible amount of passes and we needed that," said Guardiola. "Here at Burnley it is not easy. We conceded one chance in the first half but we played in a clever way and it is a good performance," he added.