Warrenpoint continue to find life back in the top tier of local football a struggle.
The newly-promoted side suffered a sixth league defeat in seven at the weekend, leaving them second bottom.
Goals from Ryan Harpur and Christopher Hegarty ensured more frustration at Dungannon.
The Swifts deserved this win, dominating both possession and chances.
Indeed, had their finishing been more clinical, the margin of victory could have been greater.
The Swifts, aiming to bounce back from the previous Saturday’s defeat at Cliftonville, made a strong start.
After 12 minutes Paul McElroy crossed to Harpur, whose close-range snapshot was well blocked by Alan Blayney.
Soon afterwards another cross found Cormac Burke, who was denied by a defender. The ball came to Ryan Mayse, who stabbed wide at the second attempt.
McElroy also sent a header against the post when well placed.
Warrenpoint’s first chance fell to Darren Murray after a corner from Neil McCafferty, but his strike was always rising.
Then Sean Mackle hit an effort from 25 yards which flashed narrowly wide.
The deadlock was broken in the 38th minute.
Liam McMenamin crossed and Mayse headed towards goal, with Harpur getting the final touch as it crossed the line.
But Warrenpoint were back in the game five minutes later.
The industrious Lorcan Forde got on the end of Mackle’s cross, edging in front of his marker to side-foot home.
Dungannon set about retaking the lead as the second half began.
Jarlath O’Rourke’s free-kick found David Armstrong, whose shot was saved, with Douglas Wilson and McElroy unable to convert the rebound.
A Mayse cross found McElroy, who was foiled by a desperate defensive block.
Murray thought he had given Warrenpoint the lead, but his classy finish from a Forde pass was ruled out for offside.
Dungannon kept the pressure up and edged ahead for the second time in the 75th minute.
Thomas Lockhart’s cross was touched on for Hegarty, and the defender reacted quickest to score with a close-range finish.
DUNGANNON: Addis, McMenamin, Hegarty, Armstrong, O’Rourke, Wilson (Hutchinson, 76), Burke, Harpur, Mayse, McMahon (Lockhart, 60, Lowe, 86), McElroy
Subs not used: Teggart, Hughes
WARRENPOINT: Blayney, Foster, Lyttle, Reilly, Wallace, M Murray, Mackle, Lynch (Roohi, 78), McCafferty (McMenamin, 71), Forde, D Murray Subs not used: Turker, McCreery, McGrandles
Referee: Tony Clarke (Newtownabbey)