Hearts remain a point ahead of St Miren and Motherwell in the race for a top six finish and it is Fir Park that the Jambos must travel to for their final William Hill Premiership match before the split.
A solitary goal scored in the second-half made the difference before more than 18,000 fans at Tynecastle as Dundee United earned narrow, back-to-back wins over the Men in Maroon in the Capital and moved on to 47 points to secure their position in the top six.
The Edinburgh combine remain on 39 points and in sixth spot with St Mirren seventh and Motherwell eighth, both on 38 points.
So, the pressure is really on after a disappointing day at Tynecastle in a match in which teenager striker, James Wilson (pictured centre), was shown a straight red card.
Earlier, Neil Critchley made four changes for Hearts, including Lawrence Shankland named on the bench, and his counterpart, Jim Goodwin made five for the game at sun-kissed Tynecastle.
The first yellow card came after seven minutes, Louis Moult for a foul on Michael Steinwender, as both sides probed for an opening in a high tempo game.
Hearts earned their first corner three minutes later after Beni Baningime won the ball in midfield, but it came to nothing.
Beningime was heavily involved as Hearts forced their rivals back and the Jambos looked for a penalty when Jorge Grant went down in the box, but play was waved on.
The home side won another corner which was again cleared but the ball was fed to Elton Kabangu who drove towards goal and Jack Walton denied the Belgian striker when he saved his strong shot.
A slick moved involving Sander Kartum found Kabangu who fired for goal and, once again, Walton saved, but the goalkeeper was under pressure soon after when Baningime won the ball in midfield and fed Wilson who shot into the side netting from an angle on the right. Then Grant tested the United goalkeeper from 25 yards.
Hearts looked the more threatening side and Wilson fired from 25 yards, Walton gathered, and the same player had a tremendous opportunity after busy Baningime found hard-working Spittal out left and he sent the ball square to the 18-year-old who hit the ball well wide.
Then Baningime dragged his right foot shot from the edge of the box wide of Walton’s right-hand post before, at the other end, Will Ferry won a free-kick 30 yards from goal but it flew wide of Craig Gordon’s post.
The Tynecastle team countered and Kabango raced onto a ball down the left before finding Wilson who was denied by a late challenge on the six yard box. Yet another chance for the home side arrived when Baningime, who was immense in midfield, set up Spittal but his finish was saved by Walton.
The complexion of the match changed after 38 minutes when Wilson was given a straight red card for a tackle on Luca Stephenson and Hearts were down to ten-men. United upped their pressure on the Jambos as the home fans let their feelings be known about the dismissal to referee Nick Walsh.
Ross Docherty, United’s skipper, had a sight of goal as the break loomed, but he blasted wide as three minutes of injury time were signalled.
Emmanuel Adegboyega joined Moult in the book four minutes into the second-half for a heavy challenge on Grant and United boss Goodwin made three changes as they moved to attack the depleted Jambos.
Seconds later David Babunski had a chance and his shot was blocked before substitute Kristijan Trapanovski was shown a yellow card. It was the Jambos turn to make a change when Cammy Devlin was introduced for Kartum but it failed to stop the Tayside team taking the lead after 67 minutes.
Sam Dalby latched on to a cross from the right to send the ball wide of Gordon and into the net. A massive blow for Hearts and a major plus for the visitors.
Devlin had a half-chance after more good work from Baningime but he was muscled out by the determined United defence and that signalled more changes from Hearts, Shankland and Calem Nieuwenhof coming on for Spittal and Grant.
Adam Forrester was denied by Walton on the right as Hearts attempted to salvage something from the game, but it was United who threatened next through Trapanovski. Gordon blocked with his foot.
Musa Drammeh replaced Baningime with eight minutes of regular time remaining and Critchley was animated on the sidelines as his men battled for an opening and they exerted strong pressure on the United rearguard but failed to reap a reward.
However, Shankland drove for goal and earned a corner and Walton raced from goal to collect and that was the closest the home side came in the dying minutes until Drammeh whipped in a cross from the right and Walton was a full-stretch to clear.
Penrice was yellow carded as the clock ticked down but it was a day which promised so much and ended in disappointment.
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