Scott Sinclair gave the Premier League champions the lead on 25 minutes, but trialist Osman Sow cancelled out the goal in the second half in a fixture marking the centenary of the stadium's Main Stand.
Aleksander Kolarov calmly tucked away a penalty with 10 minutes remaining when substitute Emyr Huws was brought down in the box, ensuring that the Citizens rounded off their tour of Scotland with victory.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
HEARTS STARTING XI: Alexander, Paterson, McHattie, Wilson, Ozturk, Gomis, Walker, Buaben, Sow, Carrick, Nicholson
PIC: Big trialist Osman Sow celebrates his goal earlier tonight against Manchester City. pic.twitter.com/gXsvqmP4ro— Heart of Midlothian (@JamTarts) July 18, 2014