Chris Holland scored his second goal in 4 days with an 6th minute sidefooted effort from 8 yards out after Andy Booth and Leon Knight had drawn defenders away from Danny Schofield's cross from the right side byline.
The Dragons gave a better account of themselves tonight and improved as the game went on but the poor weather conditions, wind and rain ruled the night, made it difficult to build attacks as the game descended into a scrappy affair after a promising first 10 minutes.
Two free kicks were the main talking points for the first half.
Kenny Irons' 10th minute free kick was going in but for David Walsh's athletic save.
Steve Thomas came back from suspension for Wrexham and he proved a tricky player as his free kick fizzed over Martyn Margetson's bar soon afterwards when Willie Miller had been pulled back.
Margetson was a key player for Town, making good saves despite the swirling wind, especially after a 28th minute Darren Ferguson free kick almost foxed the Welshman in the wind.
Ferguson wasted a free kick later by shooting his free kick straight at Margetson after Kevin Gray had to bring Craig Faulconbridge down after Nathan Clarke's lapse in concentration let the Dragons striker in for a chance on goal.
There was controversy after the interval when Hector Sam headed the ball just outside the area and collapsed under a late challenge from Martyn Margetson who had raced out of his area to try and intercept the striker's run for a hanging ball.
Demands for Margetson to be sent off from all around the Racecourse Ground were ignored by the referee who opted to book the Terriers 'keeper - he was saved by the presence of two Town defenders who had retreated to the goal line to cover.
The Terriers were not althogether under the cosh, though, and creditable chances had fallen for Andy Booth, Danny Schofield, and Kenny Irons (with a long shot which was palmed away by Walsh) before Leon Knight was twice put through late on but was thwarted by poor finishing and the Wrexham offside trap.
There was time for a late scare, however, when the Dragons' Michael Blackwood went clean through at the death but Margetson raced off his line and made the save.
In the end, the Terriers had few problems tonight despite the narrow scoreline and the scrappy nature of the match.
Wrexham (4-4-2) : Walsh, Whitley (Carey 30), Roberts, Hill, Miller, Chalk (Morrell 74), Thomas, Ferguson, Blackwood, Faulconbridge (Trundle 46), Sam
Subs not used : Whitfield, Gibson
Booked : Carey
Town (4-4-2) : Margetson, Moses, Heary, Clarke, Gray, Irons, Mattis, Holland, Schofield, Booth, Knight
Subs not used : P. Senior, Dyson, M. Senior, Hay, Macari
Booked : Gray, Clarke, Margetson, Schofield
Scorer : Holland 6
Referee : Phil Richards (Preston)
Attendance : 1,725