Wrexham striker Lee McEvilly saw his header tipped over the bar by Stags' keeper Jason White before Wrexham's stopper Anthony Williams dived to hold a low shot from Nathan Arnold.
The game pulled in Wrexham's biggest crowd of the season, helped by a bargain cut-price offer on tickets.
Matt Done nearly set-up Wrexham early on, when he skipped past two tackles and crossed for the inrushing McEvilly but White was quickly off his line to clear.
Wrexham lost striker Neil Roberts with a hamstring injury straight after the start, causing an immediate reshuffle when Mike Carvill replaced him.
Martin Gritton had Mansfield's first attempt on goal, a 30-yard pot-shot that flew over the crossbar. Bryan Hodge later aimed another long shot at the Wrexham target, this time taken low by keeper Williams.
Carvill wasted a great opening for Wrexham, allowing Alex Baptiste to force him wide after being put through by McEvilly.
Wrexham's appeals for a penalty were turned down after Done went down under a challenge with Stags' keeper White. Referee Singh awarded a free-kick just outside the area and booked the young keeper.
McEvilly stepped up to take the resulting free-kick and promptly shot against the crossbar.
Mansfield started on the attack after the interval when Simon Brown hit a great shot that Williams went full-length to keep out at the foot of the post.
From the clearance, the home side broke straight up-field. The hard-working McEvilly crossed from the left to set up a good opening for Mike Proctor who headed wastefully over from six yards.
The Stags were also off target when Gritton missed a sitter, meeting Brown's cross and heading over from close-range.