Extra-time loomed when Dickov pounced at the far post for the goal that put Blackburn Rovers into the semi-finals.
Boro manager Steve McClaren was spot on in his programme column.
McClaren wrote: "Mark Hughes is every bit determined as we are to come away with a win tonight and I am expecting a very tight and closely fought encounter.
"Just one point separates the sides in the Premiership and don't be surprised if this one goes right to the wire."
This was not a game for the purists. It was a battle between two competitive sides for 90 minutes.
The game was played at a tremendous pace with players of both teams given no time to settle on the ball.
Blackburn deserved their success. There was never any question of the visitors playing it tight and hitting Middlesbrough on the break.
Blackburn had a real go though they had a slice of luck in injury time when substitute Massimo Maccarone struck an upright with a shot.
Robbie Savage headed wide for Blackburn early in the game and Shefki Kuqi missed a scoring chance.
Middlesbrough defenders Matthew Bates and Chris Riggott had a clash of heads with Bates coming worse off. Bates received treatment but continued.
Towards half-time Savage was booked for a foul on Emanuel Pogatetz. Savage immediately protested and appeared to claim that the Boro player had spat in his face.
Middlesbrough skipper Gareth Southgate had the best first half chance for his side. He suddenly popped up in the visiting penalty area but he shot wide from seven yards.
Middlesbrough introduced substitute Stuart Parnaby for Bates at the interval.
Boro could have snatched the lead when teenage winger Adam Johnson sent the ball across the middle of the goal area. It was a definite scoring chance for Yakubu, but Middlesbrough's leading scorer failed to connect at the far post as he slid in.
Blackburn stepped up the pressure and only desperate defending prevented them taking the lead with shots by Morten Gamst Pedersen and Dickov blocked.
Yakubu shot wide for the home side while Ryan Nelsen headed past the far post for the visitors.
The ding-dong battle continued with both defences stretched.
As extra-time loomed, Blackburn booked their semi-final spot with a goal in the 90th minute.
After Parnaby had headed out, Kuqi hit the ball across the face of the goal for Dickov to score from close range at the far post.