Impressive Grove did all the damage in the first half after falling behind to an Andrew Gascoigne goal on 19 minutes.
Matt Haddrell levelled with a header from an Aiden Matranga cross five minutes later and Karl Charlton took a further minute to put Grove in front.
Haddrell scored his second on the half-hour from a Tim Sanders corner and Tom Urwin made it 4-1 at the interval.
Haddrell was twice denied his hat-trick in the second half by outstanding home keeper Danny Whatsize.
And Sheffield eventually pulled one back through Danny Winter's 71st-minute penalty after Charlton had been penalised for handball.