Richie Barker's early goal gave them the edge through the first half. He was on hand to finish at close range, turning in a cross from James Brown.
Gary Liddle would have added a second goal but his shot was matched by Michael Ingham with a great save.
Lee Roche then denied the Pool, heading off the line, to keep out Ben Clark's header from Eifion Williams's cross.
Wrexham struggled early on against the elements, making little headway against the strong wind. One of their best chances came when Lee McEvilly saw a shot held by Dimitrios Konstantopoulos who went full length to turn it round the foot of a post. Again when McEvilly seemed likely to score he shot wide from six yards and saw a header cleared off the line.
It was better for Wrexham after they changed ends and had the gale at their backs. Marc Williams volleyed too high when Chris Llewellyn set him up, then at the other end Ryan Valentine cleared a Lee Bullock header off the line following a corner and the home defence scrambled a Richie Barker cross out of the goalmouth.
Anthony Sweeney had a clear chance from a blocked clearance only to shoot wide.
Wrexham improved as confidence grew and the goal came on the hour, Llewellyn side-footing home from Valentine's cross. A shot from Matt Done was blocked before McEvilly twice saw shots cleared in a crowded defence.
In a late spell of pressure from Pool, Liddle shot wide from close in and Brown saw a shot hit a defender when he seemed certain to grab a winning goal.