A goal from Jonathan Stead gave them the victory thanks to some good work from Andy Cole and a mistake by David Weir.
The Blues defender gave Cole space on the edge of the box and he used it to peel away to the left of the goal.
The former England striker then beat Alessandro Pistone before crossing for Stead. And the youngster proved himself to be the bargain buy of the season by heading home to win the match and grab his fifth goal in ten games.
Rovers had the first chance to take the lead in the seventh minute.
An in-swinging corner from Turkish midfielder Tugay escaped the attentions of the Everton back four and former Toffees defender Craig Short rose to fire a powerful header towards goal. But keeper Nigel Martyn was equals to the task and batted the ball wide for another flag kick.
Then, from the clearance, the home side broke with Wayne Rooney on the left flank.
The England striker made himself space with a wonderful first touch before producing a measured cross to the far post. Midfielder Steve Watson was waiting to launch a fierce header towards goal but visiting keeper Brad Friedel pushed the ball away for a corner.
Thomas Gravesen swung the ball into the area from the right and left-back Gary Naysmith let fly with a looping header that went inches wide.
The Blues went close again in the 11th minute when Watson and Naysmith combined to fashion a chance for Kevin Kilbane but the Irish international's 15-yard header went sailing over the crossbar.
The next effort to send the home fans' hearts fluttering came from the impressive Joseph Yobo. Picking up the ball on the edge of the box he used his strength to distance himself from his marker before rifling in a powerful shot, once again saved by Friedel.
The game was a scrappy affair with both sides struggling to find a way through to goal.
Lorenzo Amoruso shepherded Rooney well and the tricky forward was forced wide to look for any opportunities. At the other end of the field, Stead was impressive but was well marked by Yobo.
Everton were shading possession but it was Blackburn who came closest before the half-time whistle.
Full-back Michael Gray crossed in from the left flank and found Stead in the penalty box. He managed to toe-end a dipping effort that nearly lobbed Martyn, but the Everton keeper managed to tip it over.
Everton were still under pressure when Tugay's corner found the feet of Cole. The former Manchester United star was free in the penalty box and desperately pushed the ball towards goal, but Swedish midfielder Tobias Linderoth was there to clear off the line.
This served only to liven up the Toffees and they streaked down the pitch desperate to grab a goal before the break.
And the chance came just before the referee blew. A throw in on the right hand touchline found Tomasz Radzinski racing into space past the Blackburn defence and giving himself a one-on-one with Freidel.
Right on the corner of the six-yard box he looked up and fired a left-footed effort that looked certain to break the deadlock, but once again Freidel proved himself up to the task and stretched to get a hand to the ball.
It fell for a corner and this time Rooney stepped up to try and make a difference. His curling cross was inch perfect for David Weir at the back post, but the Rovers defence managed to clear his header as far as Steve Watson.
The right midfielder decided to try his luck with a spectacular overhead kick but his enthusiasm was not matched by his precision and his effort was easily dealt with.
Everton had the better of the second half with substitute Alex Nyarko providing a driving force with a number of long-range shots, none of which troubled Friedel.
The African's first effort came in the 53rd minute when he picked the ball up 30 yards out. He launched a speedy low effort that had the keeper beaten but managed to curl wide.
His next effort came 10 minutes later from a similar distance but this time went straight into the arms of Friedel. Then in the dying moments with his side 1-0 down, he launched a dipping 30-yard shot that just skimmed the crossbar.
Rooney woke up a little in the final half-hour but could not breakdown the middle of the Blackburn defence.
The home side's display mirrored the problems they have had all season - namely a lack of a creative midfielder to provide a decisive ball for the forwards.
And when Gravesen limped off injured in the 23rd minute Everton lost much of their guile. They held onto possession but their use of it was predictable, giving the visitors little trouble.
This time last season these two sides were competing for a UEFA Cup place and both managers will be thinking long and hard over the summer months as to what went wrong this year.
MAN OF THE MATCH - JON STEAD. The 21-year-old's running, never say die attitude and keen eye for goal were a telling point in this tightly-contested bottom of the table game.