United had dominated the opening 25 minutes, with Dalby sending a shot off a post from close range and Ryan Strain and Will Ferry testing goalkeeper Robby McCrorie.
Kilmarnock managed to stem the flow of United attacks and threatened through Fraser Murray on three occasions.
Emmanuel Adegboyega thought he had broken the impasse when he headed in Strain's deep cross but the flag was quickly up and backed up by the VAR review.
McCrorie and Robbie Deas had collided as they tried to intervene on the Strain cross and the keeper would later be replaced by Kieran O'Hara.
United then took the lead through Dalby, who marked his 25th birthday with an opportunistic finish after Kieran O'Hara could only push out a David Babunski shot.
That looked like earning another win to consolidate fourth place, but Kilmarnock dug deep to find a leveller that leaves them in 10th, a point above Hearts and two clear of bottom side Hibernian.
United, whose unbeaten run extends to a fifth game, move to within five points of third-placed Rangers, who visit Ross County on Sunday.