An 87th minute equaliser from Tomas Cosgrove denied Dungannon a famous victory against the champions in their first game of 2015.
The Tyrone side had been on the verge of finally ending a winless run in this fixture stretching all the way back to early 2008.
But for the sixth time this term, they were frustrated in the closing stages.
Both managers will view this as two points dropped, albeit for different reasons.
Dungannon were just three minutes from registering what would have been a massive win in the context of their season.
Meanwhile, Tommy Breslin admitted Cliftonville’s title hopes were hanging by a thread after a fourth straight game without victory.
The draw was probably about right, and in Swifts’ situation a point against the champions must be seen as a positive result.
They frustrated the Reds for long spells, with their makeshift defensive pairing of Andrew Burns and Dougie Wilson particularly impressive.
Cliftonville’s best spells came at the start and finish of a compelling game.
Early on David McDaid was fouled outside the box by Andy Coleman. Two covering defenders meant no action was taken against the home goalkeeper, who blocked Martin Donnelly’s resulting free-kick at his near post.
The Reds thought they had taken a 14th minute lead when Joe Gormley had the ball in the net after Coleman parried Martin Murray’s strike. However, the assistant referee correctly disallowed his tap-in for offside.
Dungannon failed to test Reds stopper Conor Devlin once in a scrappy opening period.
Their best effort fell to Abby Sanusi, but the winger drilled his left-foot strike over after Jamie Glackin’s corner had been flicked on.
There was controversy when a strong challenge on Glackin by George McMullan resulted in a yellow card, with Dungannon believing the visitors’ captain got off lightly.
Views were exchanged on the touchline, as Swifts boss Darren Murphy expressed his displeasure to Breslin.
The game improved in the second period, starting with a good chance for Cliftonville.
Gormley’s effort from a tight angle was blocked by the goalkeeper, the ball reached Murray at the back post but his strike hit Cameron Grieve.
After a hassle-free opening hour, Devlin was called into action three times in as many minutes.
His first save was simple, gathering a tame effort from Kris Lowe after the teenager had glided through the visitors’ defence.
The second proved more awkward, diving to his left to push Glackin’s free-kick wide.
But Devlin’s best save came from the resulting corner, when he stretched out a glove to block Mitchell’s flicked effort.
Dungannon were growing in confidence and scored in the 75th minute.
Jamie Douglas cut in from the left, cutting past Eamonn Seydak before drilling the ball across goal for Mitchell to tap home.
It wasn’t quite as eye-catching as Mitchell’s last goal against Glentoran, but it was just as important.
However, Dungannon have a habit of conceding late in games, and their old problem struck again.
Donnelly pumped the ball into the box, James Knowles’ shot fell short but Cosgrove was perfectly placed to rifle home the equaliser.
DGN SWIFTS: Coleman, Lowe, Burns, Wilson, Grieve, McCullough, Harpur (Douglas, 64), Hutchinson, Sanusi (Hazley 60), Glackin, Mitchell (Liggett, 88)
Subs not used: S Lavery, O’Rourke
CLIFTONVILLE: Devlin, Flynn (McGovern, 41), McMullan, McDaid (McCarron, 71), Donnelly, Seydak, Smyth, Winchester (Knowles, 73), Gormley, Murray, Cosgrove
Subs not used: Donnelly, Mulvenna
Referee: Ross Dunlop (Carrick)