Victory was Pools' first of the season in League Two, with Stanley still seeking a first win, leaving them four points adrift at the foot of the table.
For the opening half hour, it was obvious why the teams occupied the bottom two spots.
But Pools took the lead in the 30th minute with the game's first chance, Andy Monkhouse rolled the ball to Jon Franks and his low shot found the far corner of the net.
Stanley had a chance to level in the 40th minute but left-back Tom Aldred headed over from close range.
And Pools scored a second two minutes later when Matty Dolan fed Luke James and he set up Monkhouse to score from 12 yards.
Monkhouse would then have a goal disallowed after the break before Stanley received a lifeline when James Gray got in behind the defence, held off Christian Burgess and clipped home.
Stanley had late chances to level - Scott Flinders saved well at his near post from substitute Connor Mahoney and the keeper then kept out a near-post effort from a short corner.