Goodwillie (grounded) knocked in a deserved equaliser for United
Hibernian threw away a two-goal lead as Dundee United's David Goodwillie scrambled a dramatic late equaliser.
Colin Nish blazed in a screamer from 30 yards before slotting home a composed finish from close range on 10 minutes.
United's Craig Conway saw his penalty saved by Grzegorz Szamotulski but the home side hit back with a Garry Kenneth header early in the second half.
Deep in injury time, an almighty goalmouth melee ended with Goodwillie ramming the ball in.
The visitors from Edinburgh spurned chances to put the game out of sight in the first 20 minutes and remain four points behind United, who have only won once in their last 10 outings.
United made a wretched start but manager Craig Levein will be delighted at the stirring nature of his side's comeback.
The hosts saw striker Jon Daly stretchered off in the opening exchanges, following an innocuous challenge from Chris Hogg.
Then, with his first touch of the ball, substitute Warren Feeney lost possession to Nish, who found the top corner of the net with a thunderbolt strike from long range.
The forward doubled his tally when Prince Buaben's awful attempt at a headed back-pass broke to Nish to slip past Lukasz Zaluska, after a clever dummy on the Polish keeper.
Only an excellent one-handed save from Zaluska prevented Nish from claiming his hat-trick within a quarter of an hour when he palmed away an awkward volley after a great delivery from Denes Rosa.
With Hibs tearing United to shreds on the counter-attack, Nish passed up a glorious opportunity when he miscued a free header from just eight yards out, sending Steven Fletcher's cross wide of the target.
Nish scored twice but was not able to celebrate a win at Tannadice
Nish later turned provider, with a fabulous, raking delivery across the face of goal but the sliding Fletcher narrowly failed to connect with his outstretched left leg, when a right-foot finish looked the simpler option.
The home side were handed a lifeline when Hogg was guilty of clambering on the back of Feeney but former United favourite Szamotulski sprung acrobatically to push away Conway's spot-kick.
Hibs looked fragile down the flanks, with midfielders Derek Riordan and Alan O'Brien offering their full-backs little protection and United skipper Lee Wilkie volleyed wide after ghosting in at the back post early in the second half.
Fletcher, who netted his first Scotland goal to seal the win over Iceland on Wednesday, saw an effort on the turn smothered by Zaluska before the home team hit back to reduce the deficit on 53 minutes.
Paul Dixon made a dash for the bi-line and sent over a deep cross for Kenneth to head home, as goal-hero Nish had gone to sleep on his marking duties.
United piled the pressure on a creaking Hibs defence and Szamotulski clawed away a drilled effort from Buaben, while Francisco Sandaza stabbed wide from just a few yards, only to have his blushes reduced by a dubious offside decision.
With giant defenders Wilkie and Kenneth joining the attack at every opportunity, United were pounding the visitors with a series of troublesome long balls and Szamotulski made two fine saves to deny Sandaza.
Hibs appeared to have weathered the storm but were punished right at the death when they failed to clear their lines and Goodwillie forced in a shot beyond a frantic cluster of players to clinch a deserved point for the hosts.
Dundee United manager Craig Levein : "I shortened my life span by another five years today.
"We were fantastic in the second half but it's concerning that we were again in a position where we hadn't performed in the first half.
"We have given ourselves some really difficult tasks. We are just about managing to get ourselves out of trouble but I don't want to keep doing this."
Hibernian manager Mixu Paatelainen : "We had chances in the first half and a couple of half chances in the second half so I'm disappointed.
"I felt we should have won the game. We had chances to kill the game off and we didn't do it.
"It's a good away point at the end of the day. It's not an easy fixture and most people would be happy to come here and get the point."
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