Spaniard Karanka worked with compatriot Deulofeu as a 14-year-old during his time as a national youth coach, and tipped him for the top all those years ago.
And the Boro boss found himself on the receiving end at the Riverside last night as the midfielder opened the scoring with a stunning solo effort and then provided the ammunition for Romelu Lukaku to head the visitors into a 2-0 lead with just 28 minutes gone — and that was the way it finished — in front of a largely shell-shocked crowd of 31,628.
“It was a fantastic occasion, to be involved in the cup,” Everton manager Roberto Martinez said.
“We had to be mature and control the game and we did that really well, especially after the Bourne- mouth result. It showed we learnt a lot.
“It is a terrific feeling to get through to the semi-final and good memory for our football club.
“Middlesbrough had a team who are good on the ball but we defended really well. All in all, the two goals were exceptional pieces of quality.
“More than anything, after keeping a clean sheet from going 2-0 up was very pleasing.”
Martinez’s men can now put up their feet briefly ahead of Monday night’s Premier League clash with Crystal Palace, while Boro must dust themselves down for a tricky trip to Ipswich on Friday evening.
The hosts went into the game having win six of their last seven games in all competitions, but knowing they would have to play to their maximum if they were to extend that against Premier League opposition, and good Premier League opposition at that.
Everton were unbeaten in five matches going into this cup clash and were in no mood to surrender that record, or even to be extended the way neighbours Liverpool were by the Teesiders last season — the Reds finally edged home 14-13 in a dramatic penalty shoot-out.
From the off, they kept the ball moving, working to drag Boro out of position and creating the gaps from which the likes of Lukaku and Deulofeu could wreak havoc.
The Championship promotion hopefuls might have taken the lead with goalkeeper Joel Robles turning away Stewart Downing’s 17th-minute free-kick before being bundled into the net along with the ball to the sound of the referee’s whistle from the resulting corner.
But the tie was effectively settled inside eight minutes as top-flight class was made to tell.
Boro simply could not get anywhere near Deulofeu as he set off from the centre circle and skipped past every approaching red shirt with the minimum of fuss before steering a right-foot shot past goalkeeper Tomas Mejias and into the bottom corner.
The Spaniard turned provider only eight minutes later, accepting Ross Barkley’s raking pass and bamboozling emergency left-back Fernando Amorebieta before delivering the perfect cross for Lukaku to glance a header wide of Mejias and in off the post.
Cristhian Stuani forced Robles into a diving save with 10 minutes of the half remaining and Kike saw a delicately chipped effort drop just wide with the keeper beaten.
However, Everton left the pitch at the break knowing they had one foot in the last four.
Robles had to tip away Downing’s stinging 59th-minute drive after Stuani’s enterprising run, and Boro saw appeals for a 64th-minute penalty for handball waved away after Emilio Nsue’s ball into the box hit Brendan Galloway.
Stuani headed just over from Nsue’s inviting cross when he really should have scored with 20 minutes remaining, but there was simply no way back for Karanka’s side as Everton marched on.
Mejias, Nsue, Ayala, Gibson (Friend 83), Amorebieta, Clayton (Adomah 73), Leadbitter, Stuani, Downing, De Pena (Forshaw 46), Garcia.
Robles, Coleman, Stones, Funes Mori, Galloway (Baines 73), Cleverley, Barry, Deulofeu (Mirallas 81), Barkley, Osman, Lukaku (Naismith 86).
Referee Roger East