The visitors threatened first when striker Gary Liddle found space in the box to fire in a shot which forced a good save from goalkeeper Josh Lillis.
Scunthorpe who should have gone ahead after 21 minutes when striker Garry Thompson had a free header in front of goal but could only rattle the crossbar.
Thompson missed another good chance for the home side early in the second half when he blasted his shot wide after being put free in to the box by substitute Jimmy Ryan.
Scunthorpe broke the deadlock on the hour when Grant cut into the box from the right and steered a left-foot shot into the bottom-far corner past keeper Scott Flinders.
Seven minutes later Grant struck again with his fifth goal in the last four games with another left-foot shot after a mistake by Andy Monkhouse had gifted him possession just outside the box.
There was no way back for Hartlepool who failed to muster anything on target in the second half.