After the disappointment of Saturday’s draw against Newcastle, which left City 11 points behind Liverpool, this was a strong reaction from Pep Guardiola’s men.
Jesus curled in a lovely opener in the 24th minute and doubled the lead just after half-time, while the third came from Rodri, who conjured one of the goals of the season for his second in the Premier League, thundering a volley into the roof of the net.
Substitute Riyad Mahrez netted his 50th Premier League goal in the 87th minute, with another replacement, Burnley’s Robbie Brady, grabbing a consolation two minutes later to deny City a clean sheet.
Rodri was one of four changes made by Guardiola from the weekend, with Nicolas Otamendi given the nod ahead of John Stones in defence, while Angelino and Bernardo Silva also started.
With key man Ashley Westwood injured, Sean Dyche gave on-loan Chelsea midfielder Danny Drinkwater his Premier League debut for the club three months after he suffered an ankle injury in an incident outside a nightclub.
Dyche tweaked his formation, with Ashley Barnes left on the bench and Jeff Hendrick pushed forward to support Chris Wood, while Aaron Lennon was preferred to Brady out wide.
The last time City visited Turf Moor in late April they needed a win to maintain their slender lead at the top of the table and ground out a scrappy 1-0 victory.
Three points this time felt just as vital, with City having only won one of their previous five matches in all competitions.
They had the ball in the net in just the sixth minute when Jesus deflected in Angelino’s shot but the Brazilian was clearly offside.
Drinkwater was showing some of the invention that Burnley fans hoped he would bring but also rust and too often his touches did not find a team-mate.
One such misplaced flick let in Kevin De Bruyne, who drove towards the Burnley penalty area before sending in a shot that was straight at Nick Pope, much to the Belgian’s frustration.
The Clarets looked relatively comfortable for the first quarter of the game but a moment of real quality saw City take the lead, with David Silva and Rodri combining to play in Jesus, who paused on the right of the area before curling a delicious shot just inside the far post, giving Pope no chance.
It was a superb way for the Brazilian to end an eight-game run without scoring.
City almost grabbed a second in the 32nd minute but Pope produced a point-blank save to deny Raheem Sterling from De Bruyne’s precision cross, while the England man was also behind a deflected effort from the influential Belgian.
Burnley’s first real opening came three minutes before the break when Lennon produced a good, deep cross, which was met firmly on the volley by Dwight McNeil – only for Wood to block his own team-mate’s effort.
City broke quickly down the other end and Pope again had to be alert to keep out Bernardo Silva’s shot with his feet.
Half-time did not disrupt the visitors’ momentum and they doubled their advantage five minutes after the restart, Jesus hooking in Bernardo Silva’s clever cross.
The forward nearly completed his hat-trick three minutes later but this time his shot from a tight angle just missed Pope’s far post.
Dyche reacted with a double substitution in the 58th minute, switching to a 4-4-2 and sending on Barnes and Jay Rodriguez, with Drinkwater taken off along with Wood.
A free-kick won immediately by Barnes allowed Burnley to register their first shot on target but McNeil’s free-kick was comfortable for Ederson.
City had taken their foot off the accelerator but they continued to probe and their third in the 68th minute was the best of the lot, Rodri unleashing a volley from 20 yards after David Silva’s effort was blocked.
That killed the game completely as a contest but Mahrez, on for Sterling, produced another precision finish to make it four before Brady took advantage of a fortunate deflection.
- Manchester City have won back-to-back top-flight away games against Burnley for the first time since March 1968.
- This was the 36th time that Manchester City have won a Premier League game by 3+ goals under Pep Guardiola – the most of any team in the competition since the start of 2016-17 season.
- Burnley have conceded 11 goals in their three home games against “big six” opposition in the Premier League this season (L3), compared to only two goals in five home games against opponents from outside the “big six” (W4 D0 L1).
- Manchester City manager Pep Guardiola is unbeaten in his nine games against Sean Dyche across all competitions (W8 D1); winning each of the last four in a row.
- Each of Gabriel Jesus’ last 11 goals in all competitions for Manchester City have been scored away from the Etihad Stadium, with the first in this run coming in last season’s FA Cup semi-final against Brighton.
- Manchester City striker Gabriel Jesus is now the third top-scoring Brazilian player in Premier League history (32), trailing only Philippe Coutinho (41) and Roberto Firmino (52).
- Manchester City winger Riyad Mahrez became the ninth different player from Africa to reach 50 Premier League goals, netting 39 for Leicester and 11 for Manchester City (177 appearances).
- David Silva has made six assists from open play in the Premier League this season; just one fewer than he managed in 33 appearances in the competition last term (seven assists from open play).