Wrexham's four-match unbeaten league run came crashing to an end while boss Dean Saunders was away on Wales duty.
Toby Little put the visitors ahead after nine minutes, sliding home Esmond James' cross at the far post.
And Little grabbed his second only two minutes later, bundling the ball home after Wrexham failed to clear.
The home side were reduced to 10 men in the second half when Lamine Sakho received a straight red card for a headbutt on James.
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Wrexham assistant manager Brian Carey:
"We started sloppy and didn't recover.
"It looked like we were going to get back into it but the sending off changed it yet again and made life difficult for ourselves.
"I've not spoken to Lamine yet but it looked reckless from where I was and inexcusable."
Wrexham: Maxwell, Spann (Taboubi 32), Assoumani, Westwood, Mike Williams (Neil Taylor 46), Obeng (Marc Williams 74), Fleming, Smith, Sakho, Gareth Taylor, Baynes. Subs Not Used: Russell, Cieslewicz.
Sent Off: Sakho (52).
Booked: Baynes, Sakho, Obeng, Taboubi.
Hayes & Yeading: Overland, Allen-Page, Cadmore, Ruby (El-Abd 25), Green, James (Palmer 71), Mulley, Marc Canham, Cochrane, Little, Sean Canham (Watkins 85). Subs Not Used: Baker, Marwa.
Booked: Mulley, Cochrane.
Goals: Little 9, 11.
Att: 2,427.
Ref: P Davison (England).
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