The home side looked in great form as they took an early lead when Andy Holt's power header from Darren Ferguson's corner skidded in off the head of defender Grant McCann and the underside of the bar.
And an angled shot by Dean Bennett nearly crept in at the far post before Shane Higgs dived to hold it on the line.
It was nearly all Wrexham through the first half as Wrexham's five outplayed the visitors' four across midfield.
The over-worked Higgs saved a deflected shot by Robbie Foy and was grateful when team-mate Jamie Victory helped put with a vital stop on the line to keep a Jonathan Walters shot out of his net.
Higgs saved another shot by Walters before Cheltenham began to get back into the game with Kayode Odejayi and Damian Spencer trying to get the Robins going against a tough home defence.
A shot by Odejayi missed narrowly and hit the sidenetting.
It took another excellent save by Michael Ingham to deny Spencer an equaliser and the keeper made two more saves from McCann and JJ Melligan.
It was a big relief by the home side when Alex Smith and Mark Jones fed Walters who turned to score the second goal from close range.