Portadown are level with champions Linfield at the top of the Irish Premiership after beating Mid-Ulster rivals Dungannon on Tuesday night.
Dungannon struck first as Shea Campbell rose to head the Swifts into a seventh-minute lead from Terry Fitzpatrick's right-wing cross.
Wesley Boyle headed the Ports level and Kevin Braniff volleyed the winner on 28 minutes from Tim Mouncey's flick on.
Braniff saw a late penalty saved by Swifts keeper Niall Morgan.
The spot-kick had been awarded when Morgan brought down striker Richard Lecky.
Before that Braniff went close when his shot struck the base of a post.
Ronnie McFall's Ports have now won four league games in a row after losing their opening fixture away to Donegal Celtic.