Crusaders coasted for most of the way at Stangmore Park and established a merited 3-0 lead, before they found themselves hanging on grimly at the end.
The first half was all about Stephen Baxter’s men but, when Swifts did eventually waken up to the task, they reduced that gap to just one and only a superb late save denied them a draw.
After a shot from Stuart Dallas cleared the bar, Jordan Owens opened the scoring when he met a cross from Gareth McKeown and headed inside the near left post.
Martin Donnelly grabbed a second Crues goal on 25 minutes.
Credit for the move goes to Dallas for charging down a Dermot McCaffrey clearance before racing into the box and crossing for Donnelly to blast home from 12 yards.
Crusaders should have been three up on 25 minutes against a Dungannon side that didn’t register a single shot in the whole of the opening half.
Ryan Mullan blocked a shot from David Rainey before goalkeeper Sean O’Neill raced off his line to knock the ball away from Owens, just as he was about to shoot.
The best chance of another goal followed immediately as Dallas unleashed a powerful drive from the edge of the box, O’Neill rising well to superbly tip the effort away.
A third goal finally came three minutes into the second half when a free from Donnelly was met at the penalty spot by Colin Coates, who confidently nodded in.
That goal provoked a response from Swifts as they cancelled the score two minutes later. Ryan O’Neill provided the cross, Timmy Adamson the flick and PJ Lavery the volley finish.
Adamson gave Swifts hopes of another comeback when he headed in Dermot McCaffrey’s free for 3-2, before another last gasp McCaffrey 25 yard free kick was touched onto the crossbar by keeper Chris Keenan.
Dungannon Swifts: S O’Neill, R O’Neill, McClean, Montgomery, Mullan, McCaffrey, McKerr, Henderson, Ward, PJ Lavery, Adamson. Subs: Fitzpatrick for Henderson 63, McMinn, S Lavery, Forker, Murphy
Crusaders: Keenan, McKeown, Bell, Magowan, Coates, Dallas, Donnelly, Watson, Caddell, Owens, Rainey. Subs – Murphy, Halliday, Arthurs, Gibson, Faulkner
Referee: M Smyth, Antrim.