First half goals from Gabriel Jesus and Raheem Sterling paved the way for a 13th consecutive victory for Pep Guardiola's men, who have now conceded just four times in their last 20 outings in all competitions.
Story of the Match
Manchester City came into the game unbeaten in their last 12 against the Clarets, with Burnley's last victory over the league leaders coming back in March 2015, when George Boyd's second-half strike secured a 1-0 victory at Turf Moor.
It's the second time the two sides have met this season, with the Citizens running out 5-0 victors when the sides met at the Etihad back in November.
It took a little over two minutes for Manchester City to make the breakthrough, with Jesus finishing from close range after Nick Pope spilt Bernardo Silva's driven effort into the path of the grateful Brazilian.
It was Jesus' second goal in as many Premier League games, having failed to find the net in his previous nine.
The early goal was a dagger through the heart of Sean Dyche's pre-match plans, and allowed City to drop the intensity a gear in a similar manner to their 1-0 win over Sheffield United on Sunday.
In fact, it was almost like a training ground session at times in the first half, with the visitors creating little in the way of chances, but dominating possession of the ball in trademark fashion.
City doubled their lead just shy of half-time, and it was oh so simple for Pep's men.
Ilkay Gundogan was played in down the right and delivered an inch perfect cross, allowing Sterling the easiest of finishes from close range.
Burnley had come from behind to see off Aston Villa in their last outing at Turf Moor, but it felt as though a minor miracle would be required for Dyche's men to turn this one around.
The second half continued in a similar vein to the first, and City ought to have extended their lead early in the second period as Sterling was sent through on goal, but Pope was out quick to deny his international compatriot.
It looked as though City had made it three moments later though as Riyad Mahrez fired home from 12 yards out, but the assistants flag was raised, with VAR confirming the Algerian was marginally offside.
There was VAR controversy on the hour mark though, as James Tarkowski looked to have brought down Jesus, Martin Atkinson waved away the claims and to the surprise of many, so did VAR.
The first booking of the night fell the way of Ederson, with the City stopper clattering into Erik Pieters some 30 yards away from goal. Such is the Brazilians eccentric style of play.
That was about as exciting as it got for Ederson though, with Burnley never testing the City back line, as the hosts ran away 2-0 victors, picking up their 13th win in a row as a result.
As for Burnley, they remain 16th, eight points adrift of safety. They welcome fellow strugglers Brighton to Turf Moor on Saturday.
Defence wins titles
It's an age old adage, attack wins games, but defence wins titles, and it couldn't be more relevant right now.
On a night where City's attack failed to sparkle, their stubbornness in defence meant that Burnley never looked like finding a way through.
Gundogan for POTY?
We're running out of superlatives to describe the German.
Gundogan divided the opinion of many Manchester City fans coming into this season, but the number eight has been the catalyst for the Citizens fine run of form in recent weeks.
He wasn't on the scoresheet tonight but it was his ball that allowed Raheem to double the lead just before half-time. Could we see the German collect the individual accolade his performances deserve at the end of the season?
At this moment in time, not many could question it.
Burnley: Pope; Lowton, Tarkowski, Mee (C), Pieters; Gudmundsson, Westwood (Benson '81), Cork (Stephens 71'), McNeil; Vydra, Rodriguez (Mumbongo 77')
Manchester City: Ederson; Laporte, Stones, Dias, Cancelo (Zinchenko 64'); Rodri, Gundogan, Bernardo; Sterling (C), Mahrez, Jesus