Hearts 0-2 Dundee United
Dundee United leapfrogged Hearts into fifth place in the Scottish Premier League with a disciplined win at Tynecastle.
Jon Daly gave the visitors the lead on 41 minutes, heading past Jamie MacDonald four mintes before half-time.
That was against the run of play as Hearts started the brighter with Rudi Skacel and Stephen Elliot threatening.
Late in the match Gavin Gunning blocked on his own line before heading a second at the other end.
Hearts made a strong start, with both Skacel and Scott Robinson making Dundee United goalkeeper Dusan Pernis save.
The home side's early dominance continued and striker Elliot had an excellent chance to open the scoring, swivelling to shoot in the box.
But from a great position he hit the ball straight at Pernis, when a fraction either side of the goalkeeper would have left him helpless.
With 20 minutes played it was Gunning who called MacDonald into action for the first time, forcing the goalkeeper to tip over a header.
Ian Black also had a volley at Pernis, but there was not enough conviction in the strike to trouble the Slovak, who held comfortably.
Despite Hearts having the better chances, and dominating the midfield, United took the lead minutes before the break.
Barry Douglas delivered a good free-kick into the box and striker Daly stooped in front of Danny Grainger to head home his 17th goal of the season.
That goal was against the run of play, and Elliot was denied an equaliser deep into first-half stoppage time when he watched his cross-cum-shot headed off the line by United defender Robbie Neilson.
Hearts had claims for a penalty dismissed in the second half when Grainger was deemed to have gone down too easily under pressure from Willo Flood.
The dominance that Hearts had enjoyed in the first 45 minutes was being snuffed out by the visitors, who were playing well defensively, not allowing any service to reach Elliot.
If not for that defensive strength, United would have lost their lead 10 minutes from the end, with both Pernis and Gunning combining wonderfully to deny Skacel and Elliot respectively.
From Gunning preventing a near-certain goal in his own box, moments later the full-back popped up at the other end to power an unstoppable header into the top corner of the net to seal a fifth away win of the season for United.
Hearts manager Paulo Sergio: "We were very poor in our offensive set-pieces and poor defending set-pieces and that made all the difference.
"All the rest was Hearts. We had four or five very good chances.
"It's a disappointing result, but we are in the right direction, playing with desire. We have to score goals and be stronger in set-pieces."
Dundee United manager Peter Houston: "It was a brilliant result. We can play better, we didn't pass the ball as well as we can and the players agreed with me.
"It's a massive three points for us. It was a hard-earned victory, rather than being like the other night. We had to work very, very hard off the ball.
"At half-time we were 1-0 up and we hadn't really done an awful lot in the game.
"I don't think Dusan Pernis had a lot to do in the second half, although Hearts had more of the ball.
"I thought we defended exceptionally well and that's another clean sheet."