Chris Curran sent Cliftonville through to the last eight of the JBE League Cup - but only after an extraordinary night of drama at Stangmore Park.
The midfielder netted the decisive kick in a penalty shootout after 120 minutes had finished 3-3.
Goalkeeper Peter Burke saved from Dougie Wilson and Andrew Mitchell as the Reds won 4-3 in the shootout to advance to the next round.
It was cruel on Swifts, who scored one of the finest goals you’re ever likely to see through Paul McElroy.
Goalkeeper Stuart Addis was handed his first start since re-signing in the summer as Dungannon made five changes from Saturday’s match.
Cliftonville, meanwhile, had Eamonn Seydak back from suspension in one of three changes.
The weekend loss had made it 26 games without a win in this fixture for Dungannon - a miserable run dating back to early 2008.
And that record looked set to continue as the Reds stormed into an eighth minute lead.
A searching pass from Jamie McGovern picked out Jay Donnelly, who fired right-footed across goal and into the far corner.
Donnelly was fortunate not to give away a penalty after appearing to handle the ball inside the box.
Cliftonville immediately broke up the pitch, with Martin Murray curling a shot just over.
James Knowles drew a crucial block from Addis, who reacted superbly to get in the way of the midfielder’s pile-driver.
Addis also denied Garrett at his near post, before blocking a low Seydak effort.
Dungannon had a wonderful chance to level two minutes after the restart, but Terry Fitzpatrick headed over from Alan Teggart’s cross.
Swifts boss Darren Murphy brought on Jamie Glackin, Andrew Mitchell and Marc McConnell in the space of 15 minutes as he looked for an equaliser.
However, it seemed Cliftonville would hold on - until McElroy’s late, late equaliser.
An effort came back off the crossbar and the ex-Hull City player was first to react, heading home to take the game into extra time.
The extra 30 minutes got off to a lively start with a goal at either end.
First Teggart fired Swifts in front with a super drive from the edge of the box to make it 2-1.
But Cliftonville were level within two minutes.
Sub Martin Donnelly broke down the left side and pulled the ball across for namesake Jay, who tapped home from close range.
Martin Donnelly then put the Reds ahead in the 12th minute of added time after a scramble.
But McElroy made it 3-3 in sensational style, lobbing the goalkeeper from inside his own area - think David Beckham all those years ago.
The match went to spot kicks - where the Reds held their nerve to advance.
DGN SWIFTS: Addis, Montgomery, Armstrong, McCaffrey, O’Rourke, Wilson, Fitzpatrick (Glackin, 57), Hazley (McConnell, 72), Teggart, McElroy, Douglas (Mitchell, 58)
Subs not used: Coleman, McCullough
CLIFTONVILLE: Burke, McGovern, Flynn, Knowles, Curran, McMullan (Catney, 75), Garrett (M Donnelly, 67), Seydak, M Murray (Mooney, 80), J Donnelly, Cosgrove
Subs not used: Bonner, McNicholl
Referee: Raymond Crangle (Belfast)