Before half time at Tynecastle, Andrius Ksanavicius headed in the only goal of the game.
City have won just three friendlies this pre-season, and have just the home match with Osasuna to come on Saturday before the Premier League season starts.
City line-up: Boaz Myhill; Sam Ricketts, Anthony Gardner, Michael Turner, Andy Dawson (Liam Cooper, 85 mins); Dean Marney (Bryan Hughes, 80 mins), Ian Ashbee (Ryan France, 85 mins), George Boateng (Craig Fagan, 59 mins), Nick Barmby (Péter Halmosi, 63 mins); Geovanni (Richard Garcia, 67 mins); Caleb Folan (Dean Windass, 46 mins).
Un-used subs: Matt Duke, Nathan Doyle.