Hearts 0-1 Dundee Utd
Dundee United ignored the speculation surrounding Blackburn Rovers and Rangers target David Goodwillie to beat Hearts thanks to a Jon Daly goal.
United adapted early to Goodwillie's absence and John Rankin sent a free kick against the crossbar.
Hearts' Stephen Elliott missed a chance before Daly headed home on 38 minutes after winning the corner by forcing a save from home goalkeeper Marian Kello.
Kello and United's Dusan Pernis both excelled in an exciting second half.
And that Daly goal proved to be the decider to ensure that Hearts have now gone 10 Scottish Premier League games without a win stretching back into last season.
The side buoyed by Thursday's Europa League draw against Paksi in Hungary had started confidently, with a Marius Zaliukas shot ricocheted off Elliott and narrowly wide before a Ryan McGowan long throw had to be flapped away by goalkeeper Pernis.
Despite the absence of talisman Goodwillie, who is in negotiations with Blackburn, United looked increasingly dangerous and Rankin sent an effort wide after Daly rolled the ball into the midfielder's path.
The visitors had strong cries for a penalty when Adrian Mrowiec pulled down Willo Flood on the edge of the box.
Referee Brian Winter appeared to think about pointing to the spot before he and his assistant decided on a free-kick that Rankin rattled against the crossbar.
Hearts could have taken the lead when former United full-back Danny Grainger pulled the ball back for Elliot.
However, the striker who had replaced the suspended Jamie Hamill in the starting line-up fired straight at Pernis before John Sutton diverted another cross from the left narrowly wide.
Daly forced a brilliant save from Kello when the striker produced a thunderous volley from a Paul Dixon cross.
The Irishman made no mistake from the resulting corner, rising to head home Flood's driven cross from 12 yards.
Hearts went close to levelling when Elliott broke clear of marker Sean Dillon but dragged his shot wide.
Garry Kenneth almost found his own net as the defender lashed clear in front of goal after David Templeton set up Elliott after the break.
Kenneth sent a header in the right direction moments later but his effort was straight at Kello after Scott Allan forced the goalkeeper to turn the ball round a post as the midfield debutant looked to steer the ball into the corner.
Johnny Russell, who had replaced Goodwillie in the starting line-up, fired just wide after a clever turn.
Templeton went one better at the other end, forcing a superb one-handed save over the top by Pernis after a pirouette of his own.
Pernis produced another excellent last-gasp save to deny Hearts substitute Ryan Stevenson and secure the three points for United.