Donegal Celtic are still without a Premiership win this season after being held by 10-man Dungannon.
Stefan Lavery put the Swifts ahead when he intercepted Kevin Keegan's headed backpass before lobbing John Connolly.
Swifts keeper Niall Morgan kept out a Conor Downey shot but Peter McCann hit the net for DC just before the break.
Matt Hazley was shown a straight red card for a rash challenge on McCann after 51 minutes but the visitors held firm to secure a point.
DC striker Mark Miskimmin was denied by Morgan as the hosts chased a winner.