Cliftonville striker Joe Gormley popped up with a late leveller to deny Dungannon victory at Solitude.
Liam Boyce beat his marker before smashing into the net to put the Reds ahead just before the break.
The Swifts hit back with Darren Boyce's half-volley hitting the bar and going in before Chris Lavery's low striker gave Dungannon a 84th minute lead.
The champions salvaged a point in the dying seconds when Gormley stabbed in from a Boyce cross.
Cliftonville dominated the first half and Niall Morgan saved from a Gormley shot before Boyce drilled in the opener after 42 minutes.
Diarmuid O'Carroll should have doubled the lead before half-time but he blasted over from six yards.
Dungannon levelled thanks to a superb Boyce strike in the 53rd minute and the visitors grew in confidence with Ryan Harpur, Jamie Davidson and Boyce going close.
Lavery fired home from 14 yards to put the Swifts in front with just six minutes left, but Gormley's close-range finish meant they had to settle for a point.