Wrexham started the game on the back foot as Huddersfield Town dominated proceedings in the first 45 minutes. The hosts created more goalscoring opportunities and could have broken the deadlock just minutes before half time. In the 40th minute, Callum Marshall set up a perfect ball for Dion Charles in the centre of the box but the forward's shot flew over the crossbar.
The Red Dragons looked more composed in attack after the break and Jay Rodriguez came close to scoring twice. In the 57th minute, Rodriguez attempted a shot from the edge of the box which was parried away by Lee Nicholls. The English goalkeeper then stopped Rodriguez's header from close range in the 67th minute to deny Wrexham from going one up.
Phil Parkinson introduced Steven Fletcher in place of Jay Rodriguez in the 72nd minute and the 37-year-old was an instant hit as within a minute, he broke the deadlock. Smith attempted a header from Oliver Rathbone's cross which was saved by Nicholls, but Fletcher was in perfect position to slot the loose ball home.
Fletcher confirmed crucial three points for the Welsh club as their nearest competitors, Wycombe picked up a win. With Birmingham City losing their fixture to Bolton, Wrexham have now reduced their gap with the league leaders to 11 points.