The ex-Jambos head coach saw the Terrors run out 3-1 winners at Tynecastle thanks to a first-half double from loan striker Jordan Robertson and a late penalty by Barry Robson.
Both sides ended the game with ten men, while Laryea Kingston recorded a late consolation for the home side, who scarcely deserved to take anything away from such a below-par performance.
Lithuanian trio Tomas Kancelskis, Andrius Ksanavicius and Andrius Velicka were all left out by the Jambos, with Jose Goncalves, Christian Nade and Calum Elliot earning starts.
Levein made only one change to the team which beat Motherwell 1-0 last time out, Steven Robb being replaced by Robertson, who broke the deadlock 14 minutes in.
The Sheffield United youngster latched onto a Marius Zaliukas mistake to slide the ball home, leaving home keeper Steve Banks with no chance.
Eleven minutes later it was 2-0 to the Tangerines as Robertson was on hand again to leave Banks stranded by rifling the ball into the roof of the net, after Lee Wilkie's aerial presence had caused confusion in the home defence.
Michael Stewart and Zaliukas went close as Hearts pushed for a way back into the game, but they were unable to make any headway, despite the presence in their side of striker Mauricio Pinilla after nearly a year out of the picture.
Just as the game seemed to be drifting to a tame conclusion Elliot was dismissed for handball and Robson added a third goal for United by converting the resulting spot-kick.
There was still time for Terrors keeper Grzegorz Szamotulski to be dismissed for handling outside his area, with Kingston taking advantage to curl home a consolation effort for a well-beaten home side.