Jermaine Johnson treated the Owls fans to a special goal after 15 minutes. Cutting inside from the left, he left two defenders bamboozled before drilling the ball into the top corner.
Former Barnsley striker Daniel Nardiello equalised in the second half, firing low under goalkeeper Nicky Weaver.
Terrible defending allowed Troy Archibald-Henville in for a late Exteter goal, before Weaver was stretchered off in the last few minutes.
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