Neville Southall, the Everton goalkeeper, made his 800th club appearance and to celebrate Rovers gave him plenty of work despite the shock of Gary Speed's seventh-minute strike for the Merseysiders with the game's first shot on target.
Duncan Ferguson headed down to Danny Cadamarteri who calmly set up the former Leeds midfielder to fire in from just inside the penalty area.
Kevin Gallacher twice went close to beating the 39-year-old Southall, whose bruised foot would have kept him out of the side were it not for the reserve keeper Paul Gerrard's more serious injury. Everton held out until eight minutes before half time when a Stuart Ripley corner was driven back in by Gary Flitcroft and Gallacher touched in his eighth goal of the season.
Rovers were without their dominant defender, Colin Hendry, for the first time this season and missed him when John Oster, Cadamarteri's half-time replacement, centred for Ferguson to put Everton back in front. But two goals in the final 10 minutes from Damien Duff and Sherwood broke the visitor's resistance.
Four wins in five matches have lifted some of the doubts about Southampton's ability to defy gravity yet again and survive in the top flight for another season. The latest win, a 4-1 rout of relegation favourites Barnsley at The Dell, saw the Saints two up in five minutes.
Matthew Le Tissier converted a third-minute penalty - Kevin Davies, who has been called into the England under-21 squad, was felled by Adrian Moses - and Carlton Palmer added the second goal two minutes later when Davies released Matthew Oakley on the left. His cross picked out the former Leeds midfielder whose left-foot volley gave the Barnsley goalkeeper Dave Watson no chance.
Davies scored the Saints' third - and his eighth of the season - when David Hirst swapped passes with Le Tissier and slipped the ball forward for Davies to score from close range.
Barnsley pulled one back before the break when Jovo Bosancic tucked away a penalty after Claus Lundekvam pulled down Andy Liddell but 10 minutes into the second half Hirst quashed any hopes when he accepted the chance set up by Le Tissier.
After six attempts, Crystal Palace still haven't won a home game in the Premiership. Yesterday they were held to a 1-1 draw by Aston Villa.
Neil Shipperley, who scored twice in Monday's abandoned match at Upton Park, gave Palace a first half lead and despite Villa's improved second- half performance looked to be cruising to a win. Then James Smith was sent off for his second booking and Julian Joachim punished the 10 men left guarding Palace.Reuse content