Skipper Lee Bullen struck in first-half injury time before substitute Andrew Talbot killed off Rovers 11 minutes from time.
Wednesday were handed a half chance on ten minutes after Rovers failed to clear Chris Brunt's cross from the right flank, Jon Paul McGovern cracked in a low shot, deflected by full-back Tim Ryan before Andy Warrington smothered the ball on the line.
Gregg Blundell forced a diving save from David Lucas before Wednesday squandered another opportunity, full-back Bullen snatching at Brunt's corner to head wide at the far post from six yards.
Rovers bounced back after a shaky start as Lucas pulled off two stunning saves in quick succession. Blundell picked out Michael McIndoe whose low drive was blocked by the Wednesday keeper, before skipper Steve Foster hit a stinging drive that was tipped over in spectacular fashion by Lucas.
John Doolan fired narrowly wide with a shot from 35 yards before Wednesday snatched the lead in first-half injury-time, Bullen jumping to meet McGovern's cross from the right to finish with a bullet header from eight yards out.
Doolan tried his luck with another long-range strike before Peacock almost grabbed a second on 48 minutes, Steve MacLean setting up the chance for the ex-Bristol City striker whose fierce shot from 20 yards was pushed away by Andy Warrington.
The Rovers keeper produced another spectacular stop this time foiling centre-back Graeme Lee as he palmed his downward header away from the foot of the post from Brunt's corner.
Substitute Talbot killed off Rovers 11 minutes from time after Peacock had headed Brunt's cross back into the goalmouth for the youngster to finish off from close range.