The Robins also stuck five goals past the Mariners with no reply, as former Premier League striker Charlie Austin opening the scoring on his debut after re-signing for his old side.
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The game stood at 0-0 as Swindon went to clear their lines following a Grimsby advance in caretaker managers Gavin Gunning and Steve Mildenhall's first game in charge.
But instead of the ball being hoofed up the pitch, it ended up hitting referee Sam Purkiss square in the face.
The official then hit the turf and stayed down until Swindon's medical team got on to help him.
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After receiving treatment, a stretcher was brought out for Purkiss, who received a round of applause from both sets of supporters as he was taken down the tunnel.
"Referee Sam Purkiss has now been stretchered off, and we're going to see a change of match official here…" Swindon Town wrote on their Twitter.
"A really unfortunate incident. We hope it's nothing serious and wish him a quick recovery. The action is back underway."
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Then just five minutes after the restart and a change of official later, Swindon's January signing Austin headed home from close range to score his first goal for the Robins since his spell there from 2009 to 2011.
Marcel Lavinier, Wales international Jonny Williams, Ronan Darcy and Saidou Khan all went on to score after the break, sealing a 5-0 win over Grimsby.
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The win takes the Robins - who lost manager Scott Lindsey and assistant Jamie Day to Crawley Town on Wednesday - up to the play-off places in sixth in League Two.
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