Cole’s fine double proved enough to break the hearts of the Second Division side but only after Rovers had emerged unscathed from a spirited second-half fightback.
However, Graeme Souness faces another touchline ban after being sent to the stands during the second half.
But he was in no mood to discuss his 57th-minute altercation with fourth official Matt Messias which led to him being banished by referee Andy D’Urso.
Souness protested fiercely about an incident involving his goalkeeper Brad Friedel but the specific nature of his complaint remained a mystery.
Souness angrily refused to comment in the press conference afterwards, saying only: “I came out to ask the linesman if he got it right when Brad came out and caught the ball.
“I don’t want to talk about it and it is not important.”
Wigan poured forward in the later stages as they strove to cancel out Cole’s clinical 16th minute opener.
Brad Friedel made fine saves from Gary Teale and Neil Roberts while Stig Inge Bjornebye was forced to clear a deflected corner off his own line on his first first team appearance in eight months.
But Rovers’ rearguard for once held firm under pressure and Cole sealed his side’s path into the last four 10 minutes from time when he raced onto David Thompson’s precise through ball and fired past John Filan.
Nathan Ellington rated Cole as one of his heroes after the draw was made but the front man sought to embarrass him by continuing his remarkable cup exploits.
Ellington had hit five goals during Wigan’s run in which they accounted for West Brom, Fulham and Manchester City.
He made a lively start, cueing up a long-range chance for Tony Dinning then bustling past Craig Short before being ruled offside.
Thompson should have put Rovers ahead when he was put through by Lucas Neill but shot across the face of goal.
Wigan were certainly not overawed and almost caught Rovers napping with an 11th minute Peter Kennedy free-kick which evaded all but Jason de Vos at the far post, who headed straight into Friedel’s arms.
Neill and Garry Flitcroft both had shots saved by Filan before Cole should have opened his account when he charged down on goal but dribbled his shot against the base of the post.
Two minutes later he made up for his miss when he raced onto a great Tugay through ball and slammed a fine shot past Filan from 10 yards.
Jason Jarrett’s suicidal hesitation in his own half should have cost Wigan in the 28th minute when his poor attempted pass sent Dwight Yorke momentarily clear.
But the alert Jason De Vos got back and teamed up with the onrushing Filan to force Yorke wide and bundle away the danger.
Dinning ended the first half with a long-range shot over the bar and the home side set about the second half with renewed vigour.
They came desperately close twice in two minutes, first when Scott Green’s corner was cleared by Bjornebye and then when Ellington’s cross was met by a Roberts header which Friedel saved at point-blank range.
Keith Gillespie should have made Rovers safe in the 51st minute when he was sent clear by Yorke but shot across the face of goal.
Substitute Teale almost became a 65th-minute hero with a super swerving shot from 25 yards which Friedel brilliantly turned around the post.
Cole raced clear but saw his shot blocked by an alert Filan before his second strike which ended the cup dream of the majority of Wigan’s stadium record 16,922 crowd.
Wigan boss Paul Jewell said he was proud of his side after their eventual exit.
He said: “I can’t ask any more of my players. We played against world-class players and our attitude was tremendous.
“The cup was always a bonus because realistically we were never going to win it and hopefully we can bounce back on Saturday because our main ambition has always been to win promotion.”
WIGAN: Filan, Eaden, Jackson, De Vos, Baines, Green (Flynn 72), Dinning, Jarrett, Kennedy (Teale 62), Roberts, Ellington.
BLACKBURN: Friedel, Neill, Short, Taylor, Bjornebye (Johansson 82), Gillespie, Thompson, Tugay, Flitcroft, Cole (Jansen 84), Yorke (Ostenstad 83).