Jon Stead equalised for the Tractor Boys before the Pilgrims had to play the last ten minutes with only ten men after substitute Darcy Blake was dismissed by referee Simon Hooper for what he deemed to be a dangerous tackle. Replays suggested that Blake did in fact win the ball.
The Pilgrims started well and Jamie Mackie was first to test the visiting defence, skipping past several players before seeing his shot deflected behind by Tommy Smith.
Ipswich also pressed as they looked to get a hold on the game, Carlos Edwards seeing his shot nodded behind by Australia international Shane Lowry.
But it was the Pilgrims that took the lead against the Championship's bottom side when Fletcher's drive from the edge of the area nestled nicely in the bottom corner to send the home crowd wild.
Fletcher's first goal of the campaign buoyed the Pilgrims and, at half-time, there seemed to be only one side in it.
Roy Keane made several changes to his side for the second half and they immediately showed promise when Jon Walters was denied by a superb Romain Larrieu save.
Play was stopped for several minutes midway through the second half when Iceland international Kari Arnason was temporarily forced off with a blow to the head.
His team-mates and of course Arnason himself claimed Walters had used an elbow but their complaints fell on deaf ears.
But in the end, the Pilgrims were the creators of their own undoing, when Gary Sawyer, under no pressure at all, attempted a poor back-pass to keeper Larrieu that was gobbled up by substitute Stead who made it 1-1.
The game looked set to peter out until Blake's sending off saw some late backs-to-the-wall defending from Argyle.