City were much the better team for most of the game but only had one goal to show for the numerous chances created.
Danilo's first-half howitzer was scant reward as the Blues failed to kill off the hosts and a late equaliser gave the Clarets a point when, on another day, they could have been licking their wounds for a heavy loss.
All in all, it was just one of those days and if any team in the Premier League has earned the right to have one every now and then, it's City who have best amount of points after 26 games in top flight history
At a rain-soaked Turf Moor, City began in a business-like fashion, knocking the ball around the pitch and confidently bypassing Burnley’s high press.
The Clarets picked up several early knocks and with just six minutes gone three home players had already received treatment for various bumps and knocks as the Blues dominated with several of the passing moves sublime.
The hosts were left chasing shadows at times and Vincent Kompany came close to connecting with Bernardo Silva’s clever dink on 14 minutes but collided with keeper Nick Pope and just lost flight of the ball.
A number of final passes in the Burnley box just fell short of their target as the Blues looked to open the scoring so when the goal did finally come, it was not the near-perfect move that had been threatened on so many occasions.
With 22 minutes on the clock, Bernardo switched flanks and was on the left of the Burnley box when he spotted Danilo and played a short pass into the Brazilian’s path and after nudging onto his favoured right foot, Danilo curled a powerful shot high and out of Pope’s reach to put City ahead.
It was a goal that Brazilian players have become synonymous with over the years and it was no more than City deserved.
Sergio Aguero, Ilkay Gundogan and Raheem Sterling all could have scored further goals and had Ben Mee’s volley gone in just past the half-hour, it would have been cruel on the Blues – fortunately Ederson was more than a more than a match, diving low to his left to push the ball around the post.
Mee came close again from a corner, arriving late and nodding the ball just wide as the Clarets served further warning that while there was just one goal in it, the match was still very much alive.
Aguero had a couple of chances to double the lead in the minutes before the break but a miscued header from close range and a tame shot from the corner of the six-yard box let the hosts off the hook.
The chances continued to come after the break as Burnley clung on with Gundogan going close a couple of times, but the football was so good you could forgive a little over-elaboration on occasion.
With an hour played, the only mystery was how City weren’t maybe three or four clear – and judging by the various reactions of Pep Guardiola, it was a genuine concern that his players had not yet put the game beyond Burnley.
The Blues nearly paid the price on 69 minutes when a Burnley attack saw the ball fall to Aaron Lennon and his powerful shot was brilliantly pushed on to the post by Ederson - another ominous sign if it was needed that the chances couldn't continue to be spurned.
Yet in City's next counter-attack, that;s exactly happened as Kyle Walker's excellent low cross found Sterling two yards out with an empty net to tap into, but he put the ball wide when it looked easier to score and fell to the ground in frustration.
Finally, Burnley made the Blues pay in full when a long ball into the box was half-volleyed home by Gudmundsson with just eight minutes on the clock.
It had been coming and though it was cruel, it was proof that if you leave the door ajar at this level, no matter how many opportunities you create, you are always susceptible to a sucker-punch.
Sterling's miss at such a crucial point of the game seemed to instil belief in the hosts that the might get something out of this game - but let's remember how many points Raheem has earned the Blues with several last-gasp winners this campaign!
What it means
City extend the lead at the top to 16 points, but if Manchester United beat Huddersfield Town later in the day, the overall lead will be reduced to 13.
Star man: Danilo
Best display yet for the Blues.
With no midweek game, City players will have a well-earned three days off before resuming training next Wednesday afternoon in preparation for next Saturday’s home game against Leicester City.
Then it’s off to Switzerland for the Round of 16 Champions League first leg clash with FC Basel.