Wrexham needed just 18 minutes to stun their Championship opponents and take the lead. Andy Cannon sprinted onto a through ball and finished strongly into the bottom corner.
However, Blackburn scored twice in two minutes to turn the game on its head. First, Sammie Szmodics turned home after a goalmouth scramble, before Sam Gallagher sprinted away from the backline and beat Arthur Okonkwo, who had rushed out of his goal and was left in no man's land, some 30 yards from his line.
And Blackburn had a third in injury time, as Szmodics ran onto a long ball over the top, controlled and finished on the half-volley to put the second-tier outfit firmly in control.
After half-time, Rovers refused to take their foot off the gas, and Sondre Tronstad took advantage of another defensive lapse, firing an effort into the top corner via a deflection.
Wrexham did everything they could to find a consolation goal, but Blackburn stood firm, and secured safe passage into the fifth round of the FA Cup.