The Citizens took the lead through a Danilo curler 22 minutes in, only to be pegged back in the closing stages - just the fourth time that they have dropped league points this term.
City should have been comfortably over the line, but a shocking Raheem Sterling miss from close range allowed Gudmundsson to snatch his side a point.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ederson; Walker, Kompany, Otamendi, Danilo; Fernandinho, Gundogan, De Bruyne; Bernardo, Aguero, Sterling
SUBS: Bravo, Laporte, Adarabioyo, Zinchenko, Yaya Toure, Diaz
STARTING XI: Pope; Bardsley, Long, Mee, Taylor; Cork, Hendrick; Lennon, Barnes, Gudmundsson; Vokes
SUBS: Lindegaard, Lowton, Nkoudou, Arfield, O'Neil, Wells, Westwood
Sean Dyche: "It's another chance for us to take on one of the super-powers of the league. We have done well against them over the season. Man City are the best side, I think, this season and they have shown that. They are a very powerful side, both home and away. But that's what we love about football. We've seen it at Burnley and outside of Burnley."
Pep Guardiola: "There are 13 games, 39 points to play for. We have a lead of 15. It's not over. We have amazing, tough games to play, for example we cannot deny how complicated it is playing at Burnley. After that we have to go to Stoke City, Goodison Park, we have games against Arsenal, Tottenham, United, Chelsea. Definitely it's not over."
BURNLEY SUBS: Lindegaard, Lowton, Nkoudou, Arfield, O'Neil, Wells, Westwood
MANCHESTER CITY SUBS: Bravo, Laporte, Adarabioyo, Zinchenko, Yaya Toure, Diaz