Shane Coney and Ryan McIlmoyle were on target as Dungannon made it two wins out of two in the Carling Premiership.
The Swifts, who narrowly escaped relegation last season, edged ahead through Coney's finish from Fergal McAliskey's cross in the 40th minute.
But Ballymena hit back straight away when Nathan McConnell forced the ball in after a goalmouth scramble.
McIlmoyle headed in the winner in the 52nd minute from another McAliskey ball to leave Dungannon joint top.
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