Wrexham made two changes from Saturday’s 0-0 draw with Ipswich Town as Kieffer Moore, returning from injury, and Broadhead started in place of Sam Smith and Josh Windass.
Gerhard Struber made three alterations to his line-up from Saturday’s 3-0 win over Swansea City as Mark Sykes, Haydon Roberts and Yu Hirakawa came in for Neto Borges, Scott Twine and Sinclair Armstrong.
Having absorbed pressure throughout against Ipswich last time out, Wrexham swiftly got on the front foot this time around.
They took the lead in stunning fashion on 16 minutes as captain James McClean and George Thomason combined on the left to find Broadhead, whose curling effort from 25 yards out flew beyond Vitek.
It sparked the game into life as both sides spurned glorious chances soon after, with Anis Mehmeti blazing over just a minute before George Dobson slid an effort wide at the other end.
The Robins ended the first half strongly and thought they had equalised when Ross McCrorie tapped into the net after Arthur Okonkwo parried Mehmeti’s deflected effort, but the goal was disallowed for a foul by Emil Riis on the Wrexham goalkeeper.
Roberts then drilled over as Wrexham went into the break with their slender one-goal advantage intact.
Struber’s men lifted the tempo in their quest to find an equaliser, although Wrexham were dangerous on the counter-attack and saw George Thomason rifle over seven minutes after the restart.
The hosts went even closer two minutes as Thomason quickly took a free-kick to set Moore free, although the forward dragged his shot inches wide.
McCrorie and Mehmeti had efforts for the away side as the game became increasingly open – with Moore and substitute Windass going close for the Red Dragons in the 69th minute.
But Thomason’s teasing delivery from a corner struck the far post before going in via goalkeeper Vitek to give Wrexham the breathing space they craved.
Okonkwo was alert to deny Cameron Pring in added time as the Red Dragons kept a fourth successive league clean sheet to move to within two points of the play-off spots.
