Rob Edwards equalised on the half hour mark, sending a cross past goalkeeper Paul Musselwhite and into the net.
But Forrester restored City's lead 6 minutes before half time, heading in Scott Wiseman's cross.
Justin Whittle added another 2 minutes after the break by meeting Nathan Peat's corner, and although Town forward Jon Newby replied soon after to pull a goal back, City held on under pressure from the visitors to win 3-2.
City line-up: Musselwhite; Wiseman, Whittle, Anderson, Burton; Regan, Melton, Russell, Peat; Forrester, Donaldson.
Un-used subs: Harvey, Byron, Tomlinson, O'Neil, Cooper.