Paul Hartley equalised from the penalty spot
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Paul Hartley rescued Hearts as their championship hopes seemed destined for a major blow amid speculation about the future of head coach Graham Rix.
Grant Brebner headed home Charlie Mulgrew's cross for Dundee United.
Hearts lacked the fluency of recent games, but Alan Archibald fouled Steven Pressley and Hartley equalised from the spot with their first shot on target.
Barry Robson was then sent off for fouling Pressley and Hearts' Julien Brellier followed for retaliation.
Hearts had made six changes following claims by players that owner Vladimir Romanov was picking the team.
Recent signings Mirsad Beslija and Jose Goncalves were out through injury, Lee Johnson missed out completely, while Andy Webster, Robbie Neilson and Deividas Cesnauskis dropped to the bench.
Hartley, Rudi Skacel and Takis Fyssas returned to the side and they were joined by Christophe Berra and new signings Ludek Straceny and Martin Petras.
Mulgrew, on loan from Celtic, was available again to provide the one change to the United starting line-up in place of the injured Jim McIntyre.
And United looked the more settled side, Hearts failing to repeat the pace and power that swept aside Hibernian and Aberdeen in their last two games.
Yet Michal Pospisil missed a great chance to put Hearts ahead when Straceny, playing on the right ahead of Petras, surged past Mulgrew.
The winger's cross found fellow Czech Pospisal six yards from goal, but the striker mis-kicked in front of goal.
Hearts paid for that when Petras gave away a needless throw-in and Brebner met a fine Mulgrew cross at the back post to bundle in the opening goal off the despairing Craig Gordon.
Slovak right-back Petras and Straceny were both cautioned either side of the break for fouls on Robson.
And Petras' unhappy debut came to an end after 55 minutes, Rix throwing on Neilson immediately after Samuel scooped the ball over the bar from three yards from a Robson corner.
Straceny followed, being replaced with Saulius Mikoliunas, and Hearts were suddenly a more lively force.
The game exploded into life in the final 10 minutes after Archibald appeared to haul down Pressley.
Hartley fired home from the spot and the game looked like it would swing Hearts' way when winger Robson was sent off for a wild challenge.
But Brellier's push on United defender David McCracken meant that the Hearts midfielder followed Robson to the dressing-room, leaving both sides to end a lacklustre game with 10 men.
Dundee Utd: Stillie, Duff, McCracken, Archibald, Mulgrew, Kerr, McInnes, Brebner, Robson, Fernandez, Samuel (Miller 90).
Subs Not Used: Samson, Kenneth, Robertson, Gardiner, Abbot, Goodwillie.
Sent Off: Robson (86).
Booked: Kerr, Duff, Samuel, Brebner.
Goal: Brebner 35.
Hearts: Gordon, Petras (Neilson 57), Pressley, Berra, Fyssas, Hartley, Brellier, Skacel, Elliot, Pospisil (Cesnauskis 65), Straceny (Mikoliunas 75).
Subs Not Used: Banks, Webster, Wallace, Aguiar.
Sent Off: Brellier (86).
Booked: Skacel, Petras, Pospisil.
Goal: Hartley 83 pen.
Att: 10,584
Ref: D McDonald