It was poor defending from the Blues who already seen two identical chances just miss, but the shock woke them up and they began to force themselves into the game.
The breakthrough came just six minutes later from Lee Carsley. Kevin Campbell broke free down the left flank and his cross gave youngster Wayne Rooney a chance to fire off a sho,t but his effort slammed into the post and bounced back into play for Carsley to tap home.
Dwight Yorkre and Andy Cole caused a few problems for Everton with a header just over the bar and a shot bouncing off the post, but it was the home side that took the lead with another moment of magic from Rooney.
Everton's dominance prompted Graeme Souness into a change of tactics just before half time. Blackburn's James McEveley was withdrawn for Keith Gillespie as Rovers switched to a 3-5-2 formation.
And after the trick worked as the match became a thrilling end to end battle, with Rooney a constant threat.
But Blackburn gave as good as their hosts with Thompson and Gillespie giving David Unsworth the runaround down the right channel.
And after a good ten-minute spell for the Blues which saw amazing runs from Thomas Gravesen and Rooney, Blackburn started to edge possession, so David Moyes adapted to Souness' tactics - bringing on David Weir for midfielder Li Tie.
And it worked until defender Lucas Neill was sent off for a second bookable offence, when ironically ten-man Blackburn began to surge forward and pepper the Everton goal with shots.
But the Blues held firm and climbed above deadly rivals Liverpool in the Premiership table with a fine performance and a win.