It happened in the 19th minute as Holloway was closing in on Chris Llewellyn, he was hit by the ball and it went into the net giving his keeper David Stockdale no chance.
Holloway, who had taken a knock minutes earlier, left the field in the 30th minute with suspected concussion.
The gallant Stockdale kept the Quakers in the match, first denying a header from Marc Williams and then going full-length to keep out a shot from Llewellyn.
Simon Johnson missed with a header early on which would have put the Quakers in front and then he missed a glorious chance in the 31st minute following a corner from Martin Smith.
The Quakers were under pressure until the 60th minute when Clark Keltie fired over the home bar from two yards and then minutes later Julian Joachim saw his shot beat Michael Ingham and go inches past the far post.
Wrexham's hard-working striker Marc Williams should have eased the nerves of the home side midway through the second half, but he mis-hit a cross from the tireless Llewellyn.
Wrexham had to survive some anxious moments towards the end with Darlington desperate to save something from the encounter, but the visitors had failed to trouble Ingham.