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Accies missed the opportunity to extend their 15-point cushion over the bottom side as United keeper Eiji Kawashima beat away Ali Crawford's late penalty.
But United are now 12 points adrift of second-bottom Motherwell.
Accies' Mikey Devlin was sent off in injury-time for a second bookable offence, but there was no time for United to press home their advantage.
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A draw was an accurate reflection of a dour match, with goal-scoring opportunities scarce,  but the point does United little good.
United have a game in hand over Motherwell, beaten 2-0 at home by Kilmarnock, but a massive game now looms when the bottom two face each other at Tannadice on Tuesday.
Though Mixu Paatelainen's side have only lost once in their last five matches, they desperately need to win games against their relegation rivals.
They may feel they were denied the opportunity to do that when referee Steven Maclean waved away their penalty claims after Coll Donaldson appeared to be tripped.
But although Accies had to survive a couple of late goalmouth scrambles, the only shot Michael McGovern had to to deal with was a poked effort by Simon Murray, which the keeper turned round the post.
Indeed, Kawashima turned out to be their hero after Dougie Imrie was adjudged to have been fouled in the penalty area with four minutes left.
Crawford, Accies' most accomplished player, fired the spot-kick down the middle but the keeper's flailing legs kept it out.
Dundee United were cast further adrift at the foot of the Premiership as they were held to a draw by Hamilton.