United had taken an early lead in Saturday's SPL clash at Tynecastle through Barry Douglas before Rudi Skacel levelled just before half-time.
Hearts then left it late again in the second half as a header from Zaliukas proved to be decisive after David Goodwillie was denied from the penalty spot in the final seconds.
The home side were boosted by the news that Lee Wallace was passed fit enough to start after being rated doubtful with a bruised ankle, while Andy Webster made his first appearance at home since his move from Rangers.
United were without the injured Craig Conway but Morgaro Gomis recovered enough from a knock to be named on the bench.
The visitors thought they had taken the lead after just two minutes when Goodwillie forced home a Douglas corner but referee Calum Murray disallowed the goal, with the striker appearing to use his arm to help the ball over the line.
United were ahead with six minutes on the clock when Goodwillie's cross was met by Douglas 10 yards out and he sent a glancing header beyond the grasp of goalkeeper Marian Kello, despite close attention from Eggert Jonsson.
The Tayside club looked more than capable of finding the back of the net again and were not too far away when a Douglas cross from the right found Garry Kenneth in front of goal and his header bounced narrowly past the post.
Goalkeeper Dusan Pernis then did well to maintain their advantage when he managed to block a deflected effort from Skacel that looked certain to leave the net bulging.
Hearts were dealt a blow when Wallace was forced out of the action after just 34 minutes and replaced by Craig Thomson.
Kenneth played on after requiring treatment to his knee following a collision with Suso Santana but admitted defeat moments later when he limped off, allowing for the introduction of new signing Timothy van der Meulen.
Hearts levelled in injury time when Stephen Elliott's shot was parried by Pernis and van der Meulen's attempts to clear fell for Skacel to bundle home the rebound.
United could have found the back of the net again after the restart when Prince Buaben cut inside from the left before rifling into the side-netting.
Johnny Russell then slipped a neat pass into the path of Goodwillie but Webster prevented him from unleashing a clean shot at goal as Peter Houston's men tried to restore their lead.
Hearts swapped Suso for Andy Driver before Russell made way for Danny Swanson following an earlier challenge from Ian Black.
With time fast running out, Driver saw efforts on goal from the corner of the six-yard box blocked twice in quick succession as stubborn defending prevented him from claiming a late winner.
The home side looked the more likely to snatch a last-gasp goal and that is exactly what happened when Zaliukas rose above everyone else in the box to power home a header from Skacel's corner with two minutes to go.
There was further drama to come deep into injury time when the referee pointed to the spot for a Palazuelos push on David Robertson in the box, but Goodwillie's poor spot-kick was blocked by Kello before he fired wide from the rebound.