A rare Ryan Fallowfield strike saw Town extend their unbeaten run to six matches after the full back's 80th minute equaliser secured a point at The Racecourse.
Town had trailed since the sixth minute thanks to Bobby Grant's finish, but the Wrexham goalscorer's second half penalty miss proved costly as Town fought back for a share of the points.
Simon Weaver named the same starting XI that overcame Ebbsfleet in front of the BT Sport cameras, with Captain Josh Falkingham partnering Warren Burrell in central midfield.
The hosts handed a perfect start to returning Manager Dean Keates as Grant opened the scoring after six minutes, converting Jason Oswell's cross from the left.
It could have been two seven minutes later as Will Smith's pass for Falkingham was intercepted, but James Belshaw was able to deny Luke Young and see his recovering defenders block the follow up.
The evening wasn't producing much in the way of chances, as Alex Bradley and Warren Burrell picked up the only bookings of a first half played mainly in the centre of the pitch.
Town's most dangerous outlet for the first 45 was the advancing Fallowfield, though his shot was blocked in a half best forgotten.
Belshaw was called into action 11 minutes after the restart, demonstrating his quick reactions to deny Grant and Wrexham a second after the forward had struck a sweet volley towards goal.
Grant then had an even better opportunity to double his tally, from the penalty spot after George Smith had conceded a spot kick, but could only blaze his attempt over the bar.
Town then began to enjoy their best spell of the game so far with Jack Diamond glancing George Smith's cross into the arms of Christian Dibble, moments before the Wrexham stopper got a hand to Muldoon's strike across goal.
An improved Town got their rewards with ten minutes to play as Diamond had shown quick feet and get to the byline, allowing Fallowfield to fire home after the low cross had only been partially cleared.
Town's best chance of a winner came five minutes later as Diamond whipped in a corner towards Will Smith, but the defender's header fell kindly to Dibble in what was the last chance for either side.
Harrogate Town: Belshaw, Fallowfield, G Smith, Falkingham, Burrell, Beck, Kiernan (Emmett 74), Bradley (Diamond 54), Muldoon, Hall, W Smith
Subs not used: Cracknell, Stead, Brown
Goals: Fallowfield 80
Booked: Bradley, Burrell, W Smith, G Smith, Beck
Wrexham: Dibble, Barnum-Bobb, Jennings, Pearson, Lawlor, Summerfield, Young, Grant, Oswell, Rutherford, Barton (Tollitt 86)
Subs not used: Szczepaniak, Redmond, Wright, McIntosh
Goals: Grant 6
Referee: L Smith
Attendance: 3,435 (33 away)