Two headed goals from David Robertson gave United a 2-0 lead after 74 minutes, but Hibs showed great spirit to come back.
Abdessalam Benjelloun pulled a goal back with a composed finish after 77 minutes and three minutes later fellow substitute Mickael Antoine-Curier equalised from the penalty spot in a thrilling finish.
Steven Fletcher took less than a minute to show his worth as he got in behind the United defence and lashed a left-foot shot across the face of the goal and narrowly wide.
Alan O'Brien beat Dillon at the other end and delivered a teasing cross, but there were none of his team-mates in the centre to take advantage.
O'Brien had the beating of Dillon for pace and he produced another great run and cross shortly afterwards, while Fletcher was just too high with his acrobatic overhead kick.
O'Brien should have done better for Hibs after Darren Dods lost the ball at the edge of his own area and Fletcher laid the ball into his path, but he blazed over the top when he should have at least make Grzegorz Szamotulski work.
Chris Hogg and Daly had to have lengthy treatment after neither pulled out of a 50-50 ball in midfield and, while Hogg was able to resume, Daly had to go off to be replaced by Garry Kenneth.
It meant a tactical switch with Lee Wilkie going up front and Kenneth slotting into central defence alongside Dods.
While all this was going on, Merouane Zemmama brought a brilliant save out of Szamotulski with a curling free-kick with the Polish keeper getting his right hand to the ball to palm it to safety.
Fletcher struck the post with five minutes of the first half left after Rob Jones had headed the ball across goal and that was as close as either side came before the break.
Fletcher missed a decent chance in front of goal early in the second half when a Kevin McCann shot broke to him but he shot wildly.
The striker was then denied by Szamotulski after Zemmama had threaded the ball through to him.
But United had their chances too. Robertson tested Yves Makaba-Makalamby with a 16-yard shot which the Belgian goalkeeper clutched low to his left.
Robertson then nodded United in front from a Dillon cross and he repeated it eight minutes later, this time heading in a Willo Flood cross.
But Hibs hit back as Benjelloun pulled a goal back after 77 minutes with a composed finish and three minutes later the home side were given a penalty when David Murphy was pulled down in the box by Dillon, which saw the United man red-carded.
Antoine-Curier kept his cool to equalise from the spot and earn his side a valuable point.