Rovers, who lost to Chelsea at the same stage of the competition last season, played some excellent free-flowing football from start to finish, dominating possession and creating plenty of chances.
The visitors opened the scoring on 11 minutes when Ceri Holland timed her run to perfection and headed home a cross from Keira Walsh.
Lorrie Doze doubled Rovers' lead when she was first to react to a loose ball in the box and Rio Hardy added a third before the break when she turned her marker to fire low past the keeper.
Rovers remained in the ascendancy after the interval, with Zara Musker making it 4-0 on 53 minutes with a fine lob from the wing, before Chloe Adams completed the rout on the hour mark with a powerful run and shot that eluded the Chelsea keeper.
Rovers' Under-17 head coach Matt Johnson said: "The team were exceptional and it’s a good sign that they can produce their best performance in the highest profile game so far this season.
"We must thank Chelsea for hosting the game at their Cobham training ground, which provided a professional and friendly environment for Centre of Excellence football to be played."
Rovers squad: Mountain, S. Hardy, Seed, Godfrey, Mallett, Musker, Holland, Walsh, Doze, Adams, R. Hardy, Williamson, Chandarana, Brannigan, Yallop, Ratcliffe, Lambe.