Fulham stormed into a two-goal lead courtesy of Papa Bouba Diop and Boa Morte. But Zat Knight scored a late own goal, and in the dying seconds Dickov shot wide as his side missed out on a point.
Fulham picked up their fourth successive win at Craven Cottage, while Blackburn have not won away in the league since September.
Despite the form book it was Rovers who started the brighter, as Fulham took time to adjust to the absence of Steed Malbranque and Carlos Bocanegra, ruled out with hamstring and Achilles injuries respectively.
The first half was sluggish as both sides failed to find a spark, but Fulham skipper Boa Morte tried his hardest to fire the home team up.
After 10 minutes he set up Bouba Diop, but the midfielder's shot was deflected wide.
And on 21 minutes Boa Morte picked out Collins John with a brilliant chip. The Fulham forward steered a diving header towards goal, but Brad Friedel made a great diving save to tip his effort over the bar.
Robbie Savage fired a free-kick just over moments later, but Brett Emerton missed the best chance of the half on 38 minutes. Dickov cut the ball back from the byline and Emerton headed wide from five yards with the goal gaping in front of him.
A minute before half-time the deadlock was broken. The influential Boa Morte swung in a left-footed free-kick and Diop nudged the ball into the corner at the near post.
The Cottagers doubled their lead seven minutes after the interval. Brian McBride picked out Heidar Helguson and as the Icelandic forward cut the ball back, Boa Morte took a touch and buried it into Friedel's net.
The goal was a hammer blow for Blackburn and their frustration began to show as David Bentley and Dickov picked up bookings.
Referee Mark Clattenberg went on to make a total of eight bookings, but Rovers never gave up hope of salvaging a point.
Chances remained few and far between, but Morten Pedersen rattled the crossbar with a free-kick, before the visitors given a lifeline in the final minute of normal time.
Dickov cut inside and crossed into the penalty area. Knight stuck out his head to divert the ball past Mark Crossley and give Blackburn renewed hope.
In the dying seconds Dickov thought he had grabbed a leveller. He cut inside from the left once again, but his curling shot drifted inches wide of the far post to ensure Fulham held on for three vital points.
Man of the Match: Luis Boa Morte
A fantastic performance from the Fulham captain was capped by a great strike which sealed a vital win.