Wrexham made two changes from Saturday’s 0-0 draw with Ipswich Town, as Kiefer Moore returned from injury, and Broadhead started in place of Sam Smith and Josh Windass.
Gerhard Struber made three changes to his line-up from the 3-0 win over Swansea City on Saturday as Mark Sykes, Hayden Roberts and Yu Hirakawa came on for Neto Borges, Scott Twin and Sinclair Armstrong.
Having withstood the pressure against Ipswich last time out, Wrexham quickly got on the front foot this time.
They took the lead in spectacular fashion on 16 minutes when captain James McClean and George Thomson combined down the left to find Broadhead, whose curling effort from 25 yards went beyond Vitek.
This breathed life into the game, as both sides quickly missed great chances, with Anis Mehmeti making a brilliant effort just a minute before George Dobson scored at the other end.
The Robins finished the first half strongly and thought they had equalized when Ross McCrory tapped into the net after Mehmeti’s deflected effort was parried by Arthur Okonkwo, but the goal was disallowed due to a foul by Emil Rees on the Wrexham goalkeeper.
Roberts then drilled over and Wrexham went into the break with their slim one-goal advantage.
Struber’s men increased the tempo in an attempt to equalise, however Wrexham were dangerous on the counter-attack and George Thomson rifled home seven minutes after the restart.
The hosts went even closer two minutes in as Thomson immediately took a free-kick and freed Moore, although the forward dragged his shot inches wide.
As the game increasingly opened up, McCrory and Mehmeti scored efforts from distance – Moore and substitute Windass went close for the Red Dragons in the 69th minute.
But Thomson’s teasing delivery from a corner hit the far post before going through goalkeeper Vitek to give Wrexham the breathing space they wanted.
Okonkwo was alert to deny Cameron Pring in extra time as the Red Dragons kept a fourth consecutive league clean sheet to move within two points of the play-off spots.
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