Cliftonville edged out the Swifts at Solitude despite finishing the Carling Premiership game with nine men.
Joe Gormley's close-range finish gave the Reds an early lead and a superb 20-yard volley from Barry Johnston made it 2-0 on 74 minutes.
Dungannon debutant Sean Friars pulled one back with a header before Aaron Smyth and Martin Donnelly were dismissed in the dying minutes.
Ronan Scannell fired against his own crossbar in a frantic finish.
Gormley blasted into the roof of net in the 11th minute after the Swifts defence failed to clear from a free-kick.
George McMullan played Donnelly through two minutes later but the winger shot low against a post.
Cliftonville deserved their lead but the remainder of the first half was scrappy with Dungannon keeper Niall Morgan saving a weak Stephen Garrett effort just before the break.
The visitors burst into life on the restart and Johnny Topley glanced a header wide before missing the target from a tight angle.
Morgan tipped over a Donnelly free-kick in the first of many fine saves from the Swifts stopper.
The keeper had no chance with Johnston's sublime strike, the midfielder chesting down before arrowing the ball into the top corner.
Dungannon hit back within a minute with John Connelly tipping Michael McKerr's cross into the path of substitute Friars, who headed in from eight yards.
The impressive Morgan kept the score at 2-1 thanks to three excellent saves in quick succession.
He denied Diarmuid O'Carroll on his competitive Reds debut and then kept out efforts from Donnelly and Ciaran Cadwell.
Smyth was sent-off for two yellows on 87 minutes and Donnelly was shown a straight red-card a minute from time after a poor challange on Johnny Montgomery.
Morgan pushed up as the the Swifts launched a final attack deep into injury time and the keeper passed inside to Topley, who saw his shot cleared off the line and onto the bar by Scannell.
The win takes Tommy Breslin's side level on points with second-placed Portadown and seven behind pacesetters Linfield.