Shrewsbury made a tremendous start forcing three quick corners with Wrexham's defence unable to cope.
Derek Asamoah caused havoc with his pace first on the right wing then on the left when he switched sides.
From one quick cross when he whipped the ball in, Stewart Drummond's shot was deflected for another corner.
Asamoah had a hand in the opening goal, crossing from the left for the tall Leo Fortune-West to escape his marker Danny Williams for a free header that gave goalkeeper John Ruddy no chance.
Wrexham, looking for their first win since December 23, broke at the other end and made a couple of chances.
Steve Evans' header was cleared over by Sagi Burton before goalkeeper Chris MacKenzie made a superb save to keep out a header from Neil Roberts.
As Shrewsbury broke forward again, Marc Tierney crossed and Fortune-West's header was parried by a relieved Ruddy before Steve Evans completed the clearance.
A 20-yard volley from Robert Garrett was met with a reflex save by MacKenzie before Shrewsbury broke away for their second goal.
It came from defensive errors when Asamoah rounded Gareth Evans, jinked past Danny Williams and hit a low shot that Ruddy half-saved on its way into his net.
Steve Evans was sent off for leading with an elbow on Dave Edwards and he now faces an extensive ban after his third red card of the season.
Fortune-West added his second goal with an easy tap in, finishing from close range after Asamoah's shot from Edwards' cross was blocked by a diving Ruddy.
It was all over as a contest before Danny Williams sparked a late Wrexham surge with a stunning 35-yard strike that went into the top corner with MacKenzie well beaten.