The Serbian stepped up to earn victory for the Premier League champions at Tynecastle on Friday.
Kolarov's winner came after Osman Sow had cancelled out Scott Sinclair's first-half opener early in the second half as City got back to winning ways following a 2-0 loss at Dundee five days' earlier.
Sinclair, who has rarely been used since moving to the Etihad Stadium from Swansea City, put the visitors ahead in the 25th minute, but the goal owed more to the good work of the Spanish duo of Jesus Navas and Alvaro Negredo.
Navas cut in from the right to feed Negredo, who in turn slid a perfectly placed pass from the edge of the area into the path of Sinclair to slot past Hearts goalkeeper Neil Alexander.
City made a host of changes during the interval and as a result it was Hearts who started the second half the sharper of the two teams.
And the Scottish Championship side were rewarded in the 57th minute when Sow beat substitute goalkeeper Willy Caballero with a cool finish after latching onto a throughball from Dale Carrick.
Hearts looked set to hold on for a respectable draw but there was to be a twist in the tale 11 minutes from time as City's 20-year-old Welsh winger Emyr Huws was brought down in the box.
Referee Steven McLean duly pointed to the spot, enabling left-back Kolarov to secure triumph for City with a confident penalty into the bottom corner, beating the outstretched arm of Jack Hamilton despite the replacement shot-stopper correctly diving to his left.
