Substitute Byron Harrison struck the opener midway through the second half for the hosts with Wycombe substitute Dean Morgan levelling from the penalty spot 11 minutes from time.
Early Cheltenham pressure saw Terry Gornell plant a header into the goalkeeper's arms before Mitch Brundle sent an effort high over the Wycombe goal.
But after being forced to defend for much of the opening half an hour the visitors almost snatched the lead when Matt McClure headed down to Max Kretzschmar who had ghosted in behind the Robins defence, but his low shot was brilliantly saved by Scott Brown.
Wycombe should have opened the scoring after 62 minutes when Steven Craig latched on to a long clearance but, with just the keeper to beat, he steered his shot against the outside of the post.
Instead it was Harrison who broke the deadlock after 68 minutes, heading in a Sido Jombati cross.
But the lead was short-lived, with Morgan blasting home his 79th-minute penalty after Jo Kuffour had been felled by Elliott.