Julian Alvarez put the Citizens in control when he scored two first-half goals on his 24th birthday, before Rodri added a third less than 30 seconds after half time.
Ameen Al-Dakhil gave the travelling Burnley fans something to cheer about when he netted a consolation strike in second-half stoppage time, but Pep Guardiola's side ran out comfortable winners on Vincent Kompany's return to his former stomping ground.
Victory for Man City has seen them climb back above Arsenal - who beat Nottingham Forest on Tuesday - into second place, and they sit five points behind Premier League leaders Liverpool who have played a game more.
As for Burnley, who have lost 15 of their 21 top-flight games this season, they remain 19th in the table and sit seven points adrift of safety following Luton Town's 4-0 win over Brighton & Hove Albion on Tuesday.
Prior to kickoff, the headline team news came from the home side as Kevin De Bruyne was handed his first start since the reverse fixture at Turf Moor back in August last year, while Erling Haaland made a welcomed return to the matchday squad after missing 10 games with a foot injury.
Guardiola made six changes in total to the City side that began the 1-0 win over Tottenham Hotspur in the FA Cup last Friday, with Ederson, Rico Lewis, John Stones, Matheus Nunes and Jeremy Doku all recalled, while Burnley boss Kompany made just the one change to the team that drew 1-1 with Luton 19 days ago, with Sander Berge replacing Josh Cullen in midfield.
Man City unsurprisingly dominated proceedings early on and it took them just 16 minutes to open the scoring courtesy of a close-range header from Alvarez.
Nunes burst down the right channel and his initial attempt of a cross was blocked by the first man, but he quickly regained possession before dinking a perfectly-weighted left-footed delivery into the six-yard box for to Alvarez to nod City in front.
Just four minutes later, City scored a second courtesy of some quick-thinking from De Bruyne, who cleverly caught Burnley off guard with a free kick rolled from the edge of the area into the path of Alvarez, who slotted a right-footed finish into the bottom-left corner with aplomb.
Alvarez's goals represent his 14th and 15th of the season, while he has now impressively netted 20 times in 24 home starts across all competitions since joining the Citizens.
Summer signing Nunes made a fine impression in the opening half hour, particularly with his bursting runs down both channels, and his powerful shot from a tight ankle stung the gloves of ex-City youngster James Trafford, who managed to swat the ball away from Burnley's goal.
Man City had their tails up after scoring two early goals and their desire to net a third was evident as they sprayed the ball across the pitch with purpose, posing a threat every time they entered the final third.
Burnley rarely had the opportunity to put their stamp on the game against a dominant City outfit boasting over 75% possession, but their best sight at goal in the first half came just two minutes before the interval when Lyle Foster cut inside from the left and fired a curling strike narrowly wide of the far post.
Man City showed no signs of slowing down and scored their third goal of the night just 26 seconds after the restart when Rodri met a pinpoint pass from Phil Foden to sweep a superb first-time strike from the edge of the area into the bottom corner.
Burnley, whose only real threat came on the counter-attack, missed a great opportunity to pull one back on the 52-minute mark when Zeki Amdouni fired a right-footed effort high over the crossbar after running through one-on-one with Ederson.
Chants of Haaland's name reverberate around the Etihad when he entered the pitch 20 minutes from time, replacing De Bruyne, but the smile on the Norwegian's face soon turned into a frown when Doku failed to spot his bursting central run towards the box, and instead played a loose ball toward Alvarez.
Tempers briefly flared when Connor Roberts clipped the heals of Stones, much to the frustration of Ederson and Lewis - both Roberts and Ederson were booked following some handbags in City's penalty box - before Haaland at the other end glanced a close-range header wide with his first real chance since coming off the bench.
Man City looked on course to keep a clean sheet, but Burnley had other ideas and pulled one back in the third minute of stoppage time when January signing David Datro Fofana - on loan from Chelsea - darted past Josko Gvardiol on the right flank before drilling a low cross to Al-Dakhil to tap the ball into the bottom corner.
Nevertheless, the Citizens produced a professional performance to see off Burnley and Guardiola's men will now shift their attention to next Monday's Premier League clash at Brentford, while the Clarets play host to Fulham at Turf Moor in their next match on Saturday.