The result was harsh on the hosts, who were dominant in the first-half, but an improved display by Blackburn in the second period ensured they are two points above the drop zone - and just four behind Fulham, who are rocking after three home defeats in a week.
The result appeared hugely unlikely for long stretches, but Fulham simply ran out of steam and were punished as Diouf and Roberts made the most of terrible defending as the game reached its conclusion.
Fulham manager Roy Hodgson - who had a largely disappointing 17-month spell in charge of Blackburn from June 1997 - went into the game calling for a reaction from his side to Saturday's 4-0 FA Cup defeat to Manchester United.
He certainly got it as they were ahead within 100 seconds.
It was criminally poor defending from Blackburn as Dempsey flicked Danny Murphy's header over Christopher Samba before rounding the Congolese's central-defensive partner, Ryan Nelson, with far too much ease and sliding the ball beyond an exposed Paul Robinson for his sixth goal of the season.
The hosts were bossing proceedings as only a fine saving tackle from Stephen Warnock denied Andrew Johnson, with Robinson stopping well from Simon Davies as Dempsey dictated the play from his position just off Johnson.
Blackburn were inches away from equalising out of the blue on 17 minutes as Warnock nearly made a decisive impact at the other end of the pitch, curling a left-footed effort onto the post with Mark Schwarzer well beaten.
Even if the opening 20 minutes had been entertaining, the game soon descended into a gritty midfield battle, only enlivened by Diouf deciding to have a running battle with referee Rob Styles, one which saw him booked after the half-time whistle was blown.
The Senegalese soon showed the other side of his character though as, with Fulham under intense pressure, he poked home from six yards after the hosts' defence left him unmarked.
Schwarzer twice denied Warnock but Blackburn grabbed the winner as Roberts turned Toni Kallio - a full-back playing at centre-half due to an injury to Aaron Hughes - with ease inside the box and lashed the ball into the roof of the net to ensure there will be at least 11 teams involved in the relegation battle for the remaining ten games of the season.