The frenetic action swung from end to end throughout, with home winger Andrew Driver and United's top scorer Jon Daly passing up the best opportunities for their sides.
However, with their superior goal difference keeping them tucked in behind the Old Firm in third, it was the visitors who would be happiest with the goalless draw.
Hearts' cutting edge was blunted in the first-half when lone striker Christian Nade was removed for his own good by manager Csaba Laszlo after being lucky to escape with only a booking for a horrific challenge on United left-back Paul Dixon.
With Ugandan midfielder David Obua being introduced in his place, the Gorgie men were always likely to struggle to create chances and in the end they had to settle for extending their unbeaten run to seven matches.
The biggest crowd Tynecastle has seen this season created a magnificent atmosphere as kick-off brought together two sides well matched in the battle for third spot.
United, themselves with only one defeat in their last 15 matches, were first to settle and they created an opening in the sixth minute.
Craig Conway had seen a lot of the ball in the opening exchanges and he drifted in off his left-wing beat, past three Hearts defenders, before swinging a right-foot shot a couple of feet over the bar.
With both teams fielding five-man midfields it was perhaps no surprise that the game too often became bogged down in the centre of the pitch but there was enough action to please the big crowd.
United manager Craig Levein had kept faith with keeper Lukasz Zaluska in spite of his decision to turn down a new contract at Tannadice in favour of an apparent pre-contract agreement with Celtic.
The Pole did not have too much to do but was brought into the play to grab Laryea Kingston's scuffed shot after 28 minutes.
Two minutes later, the match threatened to explode as the red mist descended on Nade, who brushed aside his manager's pat on the back as he headed into the dugout.
His replacement, Obua, came within a whisker of claiming the game's opening goal on the stroke of half-time but neither he nor Ruben Palazuelos could get the touch that Kingston's magnificent diagonal pass into the area deserved.
Zaluska then touched Driver's angled shot wide in the final action of the first-half and Driver almost grabbed the lead for Hearts within two minutes of the restart.
Garry Kenneth was guilty of a taking a heavy touch and allowing Driver a free run on goal but Zaluska did well to hold his eventual shot with his fingertips.
The home side were given another opportunity from a set-piece a minute later as the presence of Marius Zaliukas created havoc in a crowded box but Christophe Berra's shot hit the side netting.
The Tynecastle men had appeals for a penalty waved aside in the 52nd minute as Kenneth blocked Kingston's shot and, at the other end, Zaliukas stopped Conway's volley from reaching the target.
Christos Karipidis and Jon Daly were booked as the lively action that swung from end to end threatened to spill over.
United manager Craig Levein made the first alteration of the afternoon when he brought on Danny Swanson for the ineffectual David Roberton on the right side of a packed midfield.
And Driver should then have broken the deadlock on the break in the 69th minute but after coming inside Willo Flood his right-footed shot was straight at Zaluska.
It looked as if one goal could settle the match as play swung frantically from end to end.
And it was United who almost grabbed the lead in the 73rd minute with a well-worked set-piece.
Swanson drove his corner to the penalty spot where Daly arrived at speed but the Irishman could not find the target as he powered his header just wide of Balogh's left-hand post.
United could not make anything of two corners during a period of concerted pressure on the home goal and in the end both sides had to settle for a solitary point.