The Croatian striker took full advantage of Tim Howard's fumble to turn and put the ball into the net from the edge of the penalty area to send Rovers on their way.
The home side then set out their stall to make life difficult for the visitors, but they could have added more goals through Steven Nzonzi, Mame Biram Diouf and Phil Jones.
Paul Robinson was rarely tested but showed his brilliance in the dying seconds to keep out Phil Jagielka's goal bound, long range strike.