The hosts began brightly and had a chance on goal within the first five minutes as Ben Marshall tried his luck from 25 yards, but the ball flew wide.
Blackburn continued to threaten, with Chris Taylor and Jordan Rhodes registering decent chances, but they were nearly undone through poor defending again when Dicko seized on Tom Cairney's poor pass before forcing a save.
The game opened up towards the break as Rhodes was forced to make a goalline clearance from Danny Batth's header, but that was as close as either side came to breaking the first-half deadlock.
Just three minutes after the restart, however, Wolves struck as Dave Edwards seized on a touch from Dicko to cut inside the Rovers defence and send a clinical low shot into the bottom corner.
In the 52nd minute, the visitors were let out of jail when Richard Stearman tried to head a cross behind for a corner, but ended up heading onto his own post before the ball was cleared.
Rovers continued to have a decent spell, with Rudy Gestede lashing a half-volley wide just after the hour.
However, midway through the second half, the pendulum swung the way of the away side again as Batth sent a header over the bar in the 68th minute, while Edwards fired wide and Dicko struck the bar.
Five minutes before the end, Carl Ikeme pulled off a smart save after Rhodes had attempted to slot the ball through his legs.
Kenny Jackett's charges were able to see the game out and secure all three points, which sees them climb to eighth place, two places above Blackburn in the table.