Carrick remain bottom of the Premiership after this defeat to the Sky Blues at Seaview on Friday night.
Gary McCutcheon flicked on for Allan Jenkins to fire home a third minute opener for the visitors.
Rory Carson made it 2-0 when he burst clear from a McCutcheon pass before driving low into the bottom corner.
Shane Dolan stabbed in for Carrick on 30 minutes but McCutcheon sealed the win with a diving header from Ross Black's cross 14 minutes from time.
Jenkins hit the top corner from 10 yards to give United the perfect start.
Carson doubled the lead after 22 minutes but Carrick were soon back in the game when Dolan, who had earlier shot wide, found the bottom corner after good work from Jonathan Addis.
Ballymena striker James Costello squandered a good chance just before the break, with his tame effort easily saved by Paul Murphy.
Paul Heatley came close to a second-half equaliser when he shot straight at keeper Dwayne Nelson from a tight angle.
McCutcheon finished a flowing move by heading in and giving Ballymena a deserved win.