Pool have moved off the bottom during an unbeaten February and now lie six points adrift of safety following a third win a row.
They were never troubled against the Alex and dominated proceedings.
Visiting goalkeeper Steve Phillips - fortunate to be on the pitch after making a save outside his penalty area - put up a one-man show of defiance for most of the game.
But he was beaten after 27 minutes. Jon Franks crossed deep and Jack Baldwin's far post header was turned in from close range by on-loan Middlesbrough striker Charlie Wyke.
Alex had already beaten Pools twice this season in the league and cup, but they were never in this one.
Pools made it two-nil after 39 minutes when James Poole fed Franks and the latter squirmed through three challenges to fire low across Phillips.
The goalkeeper made fine second-half saves from Wyke, Poole and Evan Horwood and was beaten in the 90th minute when substitute Andy Monkhouse smashed the ball home after Phillips had made two stops in quick succession to deny Wyke.