Batley scored four tries in a blistering second quarter to take a 26-6 lead at half-time and kept the hammer down after the break.
Halves Cain Southernwood - who kicked seven goals - and Dom Branbani were outstanding for Batley and Joel Farrell and Tom Holmes both made eye-catching debuts.
Hooker Alistair Leek’s early try was cancelled out by Elliot Minchella’s touchdown and a Simion Brown goal.
But Leek sent Brad Day over and then Holmes, on loan from Castleford Tigers, touched down before Wayne Reittie crossed at the corner and Day sliced through for his second on the stroke of half-time.
Batley added five tries in the first 23 minutes after half-time. Brambani dummied over before Eagles were reduced to 12 men with Will Hope sin-binned for tripping the Bulldogs half-back.
Reittie scored his second in the set from the penalty, Macauley Hallett crossed and Holmes touched down from Brambani’s kick to bring up the half-century.
Michael Hayward went over on 63 minutes, but Batley got scrappy after that and Sheffield completed the scoring through a try by Dane Chisholm seven minutes from time.