Deulofeu scored the opener before setting up the second for Romelu Lukaku as Everton made light work of what was a potentially tricky tie on paper against Championship high-flyers Boro.
The Toffees have never won the League Cup and are in the last four for only the fifth time and first since 2008. Stoke, Man City and either Liverpool or Southampton await in January's two-legged semi-final.
The Everton supporters once again travelled in great number, occupying a corner section of the ground and making a right old racket ahead of kick-off at the Riverside Stadium.
There was not much between the sides in the opening exchanges, the first opportunity coming from Lukaku, who saw his close-range header on seven minutes deflected wide after Ramiro Funes Mori had headed Ross Barkley’s corner back into the six-yard box.
Middlesbrough had the ball in the net shortly after, but Christian Stuani was rightly penalised for fouling Joel Robles in the air before the ball dropped over the line.
It didn’t take long for the deadlock to be broken though, and it was a strike to remember.
Deulofeu picked the ball up just inside the ‘Boro half and drove towards the penalty area. The Spaniard twisted away from Ben Gibson and shaped to bend the ball in goalkeeper Tomas Meijas’ left corner before curling the ball into the bottom right from 20 yards.
Everton doubled their lead just after the half hour, Barkley finding Deulofeu on the right, the winger bamboozling Fernando Amorebieta with step-over after step-over before skipping to the byline and crossing for Lukaku to nod home into the corner.
It’s a combination that is proving so ruthlessly effective for Everton at the moment and put the Toffees in control on Teeside.
Middlesbrough rallied before half-time in an attempt to get back into the game. Stuani saw cross fizzing cross-shot well saved before Kike chipped wide from the edge of the box.
Everton held on though and went into the break with the same advantage they held at Bournemouth on Saturday - and we all know what happened there.
Indeed the second half began to show worrying similarities from the weekend game, Everton dropping further back and allowing Middlesbrough more possession.
Thankfully Aitor Karanka's side lacked the quality to really hurt Everton where it mattered and were restricted to efforts from distance.
The best opportunity fell to Stuani once more but he headed over when unmarked inside the penalty area. Former Liverpool winger Stewart Downing also saw a fizzing effort tipped over by Robles.
As Everton began to re-assert their control Robert Martinez threw on Leighton Baines for his first apperance since May after ankle surgery.
Deulofeu was later reaplced by Kevin Mirallas, but not before being clobbered in the face by the flying arm of Daniel Ayala, the Middlesbrough man a little lucky to escape a card from the referee.
Mirallas saw his late shot saved as Everton saw the game out, the closing stages far more comfortable than the chaos we saw at the Vitality Stadium.
The final whistle brought huge cheers from the travelling support and the revelation that a Wembley final - and the chance to that 21-year trophy drought - is now just two games away.