Albert Adomah scored twice with Diego Fabbrini also finding the target, as Aitor Karanka’s side carried over their impressive league form into the cup environment.
Last season, the Teessiders beat Manchester City and troubled both Liverpool and Arsenal in the cup competitions, and no Premier League club will fancy encountering them in the fourth round on the evidence of their form so far this season.
Middlesbrough went into the game on the back of an impressive weekend win at Nottingham Forest, and while they were not at their most fluent in a scrappy first half, they deserved their advantage at the interval.
With Carlos de Pena making his debut on the left-hand side and Adam Forshaw making a rare start alongside Grant Leadbitter at the base of midfield, it was the 26th minute before either side exerted any real pressure.
Leadbitter whipped in a dangerous corner from the left-hand side, and with Boro throwing plenty of players into the box, Wolves full-back Matt Doherty almost hooked the ball into his own net.
George Saville drilled well wide for the visitors but, as the first half wore on, Middlesbrough gradually began to display more fluency.
Adomah narrowly failed to connect with Kike’s floated cross from the left-hand side, but when he was presented with a better opportunity eight minutes before the break the winger successfully broke the deadlock.
De Pena’s cross caused confusion in the Wolves defence, Ethan Ebanks-Landell panicked and made a hash of his attempted clearance, and Adomah gleefully swept home the loose ball from inside the penalty box.
Middlesbrough are currently second in the Championship and their second-half display contained many of the attacking attributes that have made them many people’s favourites to win promotion to the Premier League this season.
The Teessiders came close to doubling their lead when Kike’s shot was blocked on the edge of the area shortly after the interval, but they did not have to wait too much longer to claim a two-goal advantage.
Adomah crossed from the right-hand side, De Pena produced an excellent dummy that threw the Wolves defence, and Fabbrini swept home a crisp finish from close to the penalty spot.
Wolves boss Kenny Jackett threw on Benik Afobe and Adam Le Fondre in an attempt to change things, but any hopes of a comeback were eradicated when Boro stretched even further clear in the 64th minute.
George Friend’s cross from the left-hand side found Adomah in plenty of space at the back post and the winger drilled a precise finish into the corner.
It was Adomah’s third goal since he was restored to the starting line-up following a bust up with Karanka, and last month’s transfer request is now well and truly forgotten.
Middlesbrough: Mejias, Amorebieta, Kalas, Friend, Adomah, Nsue, Leadbitter, De Pena, Forshaw, Fabbrini, Garcia. Subs: Agazzi, Gibson, Clayton, Stephens, Downing, Reach, Nugent.
Wolverhampton: Ikeme, Doherty, Deslandes, Ebanks-Landell, Iorfa, McDonald, Saville, Price, van La Parra, Wallace, Enobakhare. Subs: Golbourne, Henry, Afobe, Rowe, Ojo, Martinez, Le Fondre.
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