Richie Humphreys gave them a great start when he smashed the ball in from Adam Boyd's cross and then Anthony Sweeney saw a shot tipped over the bar as Andy Dibble made a superb save.
Sweeney made up for that when he cut inside and ran on to a ball from Joel Porter to hit a powerful shot which the Wrexham keeper couldn't stop, although he got the hand to it as it flew into the net.
Juan Ayestarán Ugarte raised Wrexham hopes briefly when he pulled a goal back.
He was in the six-yard box to tap in after Craig Morgan headed back from Darren Ferguson's free-kick.
Hartlepool quickly restored their two-goal lead when youngster Morgan slipped and Boyd ran through to give Porter an easy goal.
Boyd added the fourth, a cool shot across the goalkeeper after Humphreys broke on the left to set him up.
Wrexham came out as if they meant to do better in the second half and Hector Sam was out of luck when his 20-yard drive took a deflection past the post.
Ugarte tried a shot that Michael Nelson blocked and the loose ball ran out to Andy Holt for a second attempt on goal from two yards out but Dimitrios Konstantopoulos was quickly down to save.
Sam led the next attack and again was out of luck when another shot was deflected for a corner.
Hartlepool came back to claim their fifth goal, taking advantage of slack defending.
Eifion Williams whipped a cross into the middle and Sweeney was on hand to drive it home.