Garry O'Connor gave Hibs the lead but United turned the tide in a manic five-minute spell. Jon Daly levelled the scores, tapping in from close range after a John Rankin shot. Danny Swanson then gave the visitors the lead as coolly fired past Graham Stack and Daly stooped to make it 3-1 after 67 minutes.
But the home side showed outstanding character to bounce back through an own goal from Scott Robertson and a super Junior Agogo finish to salvage a draw from a thrilling encounter.
Peter Houston will struggle to fathom how his side threw away such a commanding position, while Hibs - despite being yet to record a home league victory this campaign - have now gone four matches without a defeat.
It was the visitors who passed up a terrific opportunity to open the scoring after just seven minutes. Some sloppy defending allowed Scott Robertson to find Rankin on the edge of the box. The former Hibs battler flicked the ball to Swanson, who dragged his shot wide.
Rankin went within a matter of inches of putting the Arabs in front on 20 minutes, capitalising on an Ian Murray short back-pass but his lob was too high.
And United paid for their profligacy moments later. Agogo produced a marvellous through-pass, cutting through the Dundee United defence for O'Connor to run onto, and the in-form frontman calmly rounded Dusan Pernis and slotted home despite a prohibitive angle.
The lead lasted less than 10 minutes as Dundee United hit back through their captain Daly, but much of the credit must go to Rankin, turning in an excellent display on his return to Leith.
The 28-year old produced a good low drive across Stack which the keeper parried but only succeeded in pushing the ball to Daly who gratefully tapped home.
Rankin was once again the creator as United took the lead, bursting through a powderpuff Hibs midfield and slotting a perfectly weighted pass to Swanson, allowing the midfielder to slip the ball past Stack for his third goal of the season.
The game looked to be dead as the second half progressed when United increased their lead. Paul Dixon delivered a sumptuous cross to the back-post, allowing Daly to stoop and head home to give the visitors a handsome lead going into the final 20 minutes - and prompting something of an exodus of home fans.
Those fans were to miss a remarkable turnaround. Hibs halved the deficit minutes later as a poorly defended corner kick landed at Isaiah Osbourne's feet, and he kept his composure to fire in a low shot which Robertson turned into his own net.
Hibs then found the equaliser almost immediately. A through-ball from O'Connor evaded Gavin Gunning and Agogo showed good pace to beat the former Motherwell defender before slamming an effort into the corner of the net.
Rankin and Victor Palsson exchanged efforts from distance in the latter stages, both of which were easily saved to ensure a share of the points.