Twice trailing by two goals, Stevie Campbell's charges held their Firhill counterparts to a draw tonight after a great second half fight back.
United were second best for almost all of the first half with Thistle deservedly going in front after 21 minutes.
Declan McDaid made a surging right wing run before firing in a cross which Polish keeper Michal Szromnik punched out, only for the ball to fall to Kevin Nesbitt who rolled the ball into the path of Simon Colina to drill home from 12 yards.
Four minutes later, United were two down when Nesbitt curled home a free-kick from the edge of the box.
However, right on half-time the Tangerines were offered a lifeline when, against the run of play, they pulled one back, Adam Harwood heading home a Connolly corner.
But five minutes after the restart, Chris Dillon restored the hosts' two goal advantage with an angled left-footed drive from 15 yards which went in off the post.
Refusing to lie down, Connolly twice brought saves out from Basalaj.
And after 71 minutes, Ali Coote reduced the deficit, firing home from the narrowest of angles via the far post.
United chased hard for an equaliser and the lively Connolly completed a remarkable turnaround by slotting home a cross from Jamie Montgomery.
Dundee United: Szromnik, Spittal, Wilson (B Smith 61), Telfer (Montgomery 75), Harwood, Ballantyne, Connolly, S Smith, Moore (Adeymo 61), Fraser, Coote
Substitutes: Zwick, H Souttar, B Smith, Malaga, Tumilty.