Leon Knight's double gave the Bannsiders victory in the Premiership Section B encounter at the Showgrounds.
Coleraine keeper Gavin Cullen saved a Michael Ward penalty before Dermot McCaffrey headed Dungannon ahead on 11 minutes.
English striker Knight fired in the equaliser after good work from Stephen Carson and Darren Boyce.
Knight met Ryan Doherty's hanging cross to guide a header into the net for the winner after 43 minutes.
Dungannon won a controversial fifth minute penalty after Cullen's challenge on Ryan McIlmoyle.
McIlmoyle provide the corner for McCaffrey's opener while Terry Fitzpatrick and Conor Forker went close for the visitors.