The perfect 49th birthday present for boss Ally McCoist.
Caley had their moments but failed to take advantage of a nervy looking Hoops rearguard.
Garry O'Connor gave Hibs the lead but United turned the tide in a five-minute spell.
Jon Daly levelled then Danny Swanson gave the visitors the lead before Daly made it 3-1 after 67 minutes.
But the hosts bounced back through goals from Isaiah Osbourne and Junior Agogo to salvage a draw.
Aberdeen still remain without an away goal in league so far this campaign.
St Mirren moved up to fifth after disposing of Kilmarnock 3-0.