Coleraine suffered a seventh straight Premiership defeat as Dungannon scored two second-half goals at the Showgrounds to heap further pressure on Bannsiders boss Oran Kearney.
The home side missed a series of first-half chances although Dungannon's Ryan Harpur did hit the woodwork.
Coleraine were made to pay in the second half as Terry Fitzpatrick bundled the Swifts ahead on 60 minutes.
Stefan Lavery doubled Dungannon's lead 10 minutes from time.
In the build-up to the second goal, the assistant referee had raised for the flag for an apparent offside but referee John Deighan correctly ruled that the ball had come back off a Coleraine player and Lavery held his composure to beat keeper Wayne Drummond.
Dungannon started without their on-loan Coleraine striker Darren Boyce who was not able to line out because of his connection with the Bannsiders.
Coleraine started the brighter with Ruairi Harkin directing midfield affairs and Eoin Bradley looking lively.
The Derry GAA player was denied by Gareth Buchanan while Gareth Tommons was also inches wide with a long-range effort before Hazley hit the woodwork at the other end from a free-kick.
Aaron Canning squandered Coleraine's best chance of the game just before the break as he pulled his shot wide after being set up by Bradley.
Coleraine continued to press after the restart with substitute Stephen Carson and Bradley going close.
After their missed chances, it was little surprise that the struggling Bannsiders were made to pay with Fitzpatrick scrambling home from close range after the Coleraine defence had failed to clear Hazley's corner.
The decisive second goal came on 80 minutes as Lavery fired to the net.