Paul Heatley's first-half goal ensured that Crusaders stay top of the Irish Premiership on goal difference.
Heatley turned inside the box and struck a right-foot shot past Sean O'Neill after Fra Brennan failed to clear O'Neill's early long clearance.
The victory over the Swifts at Stangmore extended the Crues' unbeaten run in all competitions to 22 matches.
In the second half, O'Neill tipped away Ryan Harpur's goal-bound free-kick and Matt Hazley headed inches wide late on.
Dungannon went in to the game on the back of three straight victories, but when defender Brennan missed the ball completely, the in-form Heatley was on hand to score his fourth goal in three games.
"We are a very united team and we're working hard for each other," emphasised goal-scorer Heatley after the game at Stangmore Park.
"As league leaders, we are there to be shot at, but we are enjoying the pressure that comes with that."