The Swifts fought back with James Knowles cancelling out Adam Wixted’s opener before McBrien struck to secure a valuable three points.
The home side made a bright start to the game with Alan O’Sullivan causing a few problems for the Swifts.
It took a great tackle from Keith Cowan on 15 minutes to prevent him from getting a shot away in the box.
Thomas Maguire then was denied twice in quick succession as we approached the half hour as both Knowles and Cathal McGinty produced great blocks to deny the Point man.
Cowan then found himself in the book for bringing down Maguire as the front man threatened to break clear.
Andy Coleman was a half time sub for the hosts replacing Conor Mitchell between the sticks.
The big keeper had been struggling after picking up a knock early in the first half following a collision with his own player.
Warrenpoint continued to pose the greater threat with Daniel Byrne forcing Declan Dunne into a save from a corner on 50 minutes.
The deadlock was broken before the hour mark and it came from Point new boy Adam Wixted.
A long ball forward caused confusion in the Swifts defence and Wixted got an effort away, which found the net despite Dunne’s best efforts.
The lead lasted only five minutes though as the visitors drew level in some style.
Midfielder Knowles stepped up and curled home a delightful free kick from fully 30 yards.
As we moved into the closing stages Dunne produced two important saves to keep the hosts out.
And it was to prove vital as Dungannon edged in front with five minutes to go as Knowles teed up McBrien to fire home.