City found themselves two goals behind against Martin Allen's awkward team. But they managed to pull a goal back in first-half stoppage time and, seconds later, a spot-kick after Sean O'Hanlon was ruled to have handled.
Forrester struck the penalty low and hard but keeper Adolfo Baines made a diving save and the Dons went on to clinch victory, despite having Izale McLeod red-carded in the 56th minute.
Dons got off to a great start, winning a fifth-minute penalty, when Mark Stallard held down O'Hanlon inside the box. Stallard was booked and McLeod sent Lincoln keeper, Alan Marriott, the wrong way from the resulting penalty.
Five minutes later McLeod burst into the Lincoln box and appeared to be tripped by Adie Moses but referee, Anthony Taylor, controversially yellow-carded the Dons striker for diving.
Dons controlled the midfield, preventing Lincoln from playing their usual style of football and they went further ahead in the 26th minute when a cross from Gareth Edds was headed in at the far post by Aaron Wilbraham.
Lincoln posed few problems until the 42nd minute when a cross from Nicky Eaden found Martin Gritton, but from six yards out, the substitute headed over.
Lincoln pulled a goal back in the first-half stoppage time when Lee Frecklington hit a left-foot shot from 30 yards into the top corner. Seconds later Forrester missed his penalty and Dons were relieved to be ahead at the break.
Lincoln cracked again in the 54th minute when a cross from McLeod was met at the far post by Clive Platt, whose header flew into the net.
Two minutes later McLeod chased a long ball forward and deliberately handled. He was given his second yellow card of the game, leaving Dons to play a man short for the final 34 minutes.
Lincoln stepped up the pressure and a neat flick from Forrester put in Lee Beevers who scored from close range in the 58th minute.
Jeff Hughes was inches away from an equaliser and then Nicky Eaden headed a cross goal from close range.
Lincoln had more chances in the closing minutes with Ryan Amoo firing over and then Frecklington failing to hit the target from inside the box.
But Dons hung on during the final six minutes of time added on which was interrupted by a two-man pitch invasion.
When play resumed, Dons substitute, Scott Taylor, broke clear but was denied by an excellent save from Marriott.