A delightful pass from Tugay sent the ex-United frontman into the box and with the utmost ease, he lifted his shot over Fabien Barthez.
However, a quickfire double from the ever-dependable Paul Scholes put United in charge of the tie before half time and Ruud van Nistelrooy finished the scoring with 14 minutes left from the penalty spot.
It was only an exceptional performance from goalkeeper Brad Friedel that kept the United score down but in truth, further goals would have flattered the Red Devils.
Scholes' leveller in the 29th minute was surrounded by controversy.
Blackburn's key winger, Damien Duff, limped off before Scholes fired home from close range just before the break.
Friedel produced top-class saves from Ryan Giggs and Roy Keane at one end but Cole could have done better when he headed straight at Barthez on the hour. A goal then would have made it interesting.
As it was, van Nistelrooy sprang the offside trap in the 76th minute, was brought down by Friedel and duly smashed home the penalty.