After controlling the opening period Fulham went 1-0 up in the second half through George Williams only for Lewis Mansell to level for Rovers three minutes later.
Joe Grayson (pictured above) and Willem Tomlinson put Blackburn 3-1 up, with Williams's second goal for Fulham not enough.
Blackburn are in fifth place, the final position in the end-of-season play-offs for promotion to Division 1. They are one point above West Ham United in sixth and two ahead of seventh-placed Aston Villa, who can overtake them with victory when they meet Rovers in their last match of the regular campaign on Monday 24 April.
Fulham are fourth, two points above Blackburn and three ahead of West Ham United in sixth with a vastly superior goal difference, meaning their play-off place is all but secured prior to their encounter with runners-up Wolverhampton Wanderers on 24 April.