Striker Michael Proctor scored in the 70th minute, his 15-yard free-kick went low through the Stags wall and left keeper Carl Muggleton a spectator.
Wrexham showing all signs of nerves throughout were dealt a cruel blow in the 53rd minute when a shot by Keith Briggs struck team-mate Micky Boulding and went past the stranded Gavin Ward.
Chris Llewellyn forced a save from Muggleton and Mike Williams flicked a chance wide of the target, but just before Proctor's goal Briggs and then Jefferson Louis both shot wide and wasted chances of putting the visitors in the driving seat.
The first half was one long yawn not helped by the bumpy pitch and swirling winds and Silvio Spann saw a shot deflected away from the Stags goal and then team-mate Jeff Whitley shot wide.
Keeper Ward's only real save of the first half was to deny Gareth Jelleyman in the 22nd minute. Just before half-time Drewe Broughton put Llewellyn through on goal, but the Dragons striker shot wide.
The Stags came close to winning all three points in the last minute, but thankfully for the home side substitute Nathan Arnold shot wide.
Wrexham had started the second half showing more energy though they had to survive an early shot from Boulding, before Proctor produced an overhead hook shot which Muggleton did well to save.
Wrexham, who now face games against fellow strugglers and have games in hand on most, will have to improve in midfield as this ineffective display only put more pressure on the defence in which Richard Hope, returning after injury, led the way.