In a hard-fought contest, clear cut chances were at a premium and, despite a late surge by the home side, they couldn't find that elusive goal.
Even if Hearts close the three-point gap on fifth-placed Hibs in Sunday's final game of the season against Celtic they are 11 goals worse off in terms of goal difference.
Dundee United were presented with the first chance after just five minutes although it appeared to take striker Jon Daly by surprise.
The visitors were awarded a free-kick after Ian Black impeded David Goodwillie and Craig Conway floated the set-piece into the box. Daly was left unmarked but his touch let him down as the ball bounced off him and was gathered by goalkeeper Jamie MacDonald.
Lee Wallace was Hearts' main threat during the early exchanges with a series of forays down the left flank. His drive across the box in the 15th minute was just missed by his team-mates but Eggert Jonsson retrieved possession.
The Icelandic internationalist set-up Ian Black in the area but the midfielder blasted a shot well wide.
Hearts keeper MacDonald was then called into action to push Garry Kenneth's downward header from Conway's corner behind.
Hearts responded with a counter-attack led by Suso Santana but David Templeton blazed a shot well over from the edge of the area after accepting the Spaniard's pass.
The ball then fell kindly to Santana 18-yards from goal from Prince Buaben's attempted clearance, but his tame left-footed shot posed no danger to Steve Banks.
Conway was again the provider for United's next chance as former Hearts defender Andy Webster rose to meet his diagonal free-kick but his header was deflected wide by Wallace.
Hearts survived a major scare in the 31st minute when Goodwillie picked out the unmarked Conway in the box. After staying on his feet despite an apparent nudge from Jonsson, the winger's low shot was expertly saved by MacDonald.
From the rebound Conway was quickly back on his feet but his second attempt was deflected behind for a corner.
Webster had the ball in the net minutes later but he was adjudged to have fouled Wallace before heading home Conway's free-kick.
United manager Peter Houston made a half-time alteration with Webster being replaced by Danny Swanson, a change that saw Sean Dillon tuck in at centre half and David Robertson move to left-back.
Hearts' appeals for a penalty were turned down by referee Stephen Finnie after Calum Elliot fell inside the box under a challenge from Kenneth as the pair tussled for Jonsson's cross in the 50th minute.
Seconds later at the opposite end, Goodwillie skinned Marius Zaliukas in the box but his low drive across goal just missed the target.
Hearts made a change of their own with Ryan Stevenson having little success as a makeshift striker.
Stevenson reverted to midfield as Ian Black made way for Gordon Smith.
Former Hearts stopper Banks made a great save in the 66th to push away Templeton's stinging drive.
Santana burst forward and teed up the winger, whose effort took a slight deflection off Keith Watson.
That was followed by Stevenson hitting a half-volley just inches past the post from 25 yards after meeting Ruben Palazuelos' pass.
Santana's foul on Dundee United midfielder Conway just over 20 yards from goal gave the Tannadice side another chance to test MacDonald but
despite successfully getting the ball over the wall, Conway's effort was well held by the goalkeeper.
With the minutes ticking by, their was a sense of urgency to Hearts' play as they looked to bolster their European ambitions. Striker Gary Glen and right-back Jason Thomson were both introduced to the action, taking over from Stevenson and Santana.
The hosts lofted countless high balls into the box but they were unable to find a winning goal.