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.
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 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 wide for the visitors but, as the half wore on, Middlesbrough gradually began to display more fluency.
Adomah narrowly failed to connect with Kike’s floated cross, 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.
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 dummy that threw the Wolves defence, and Fabbrini swept home a crisp finish.
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 further clear.
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.
Middlesbrough: Mejias, Amorebieta, Kalas, Friend (Stephens 74), Adomah, Nsue, Leadbitter (Clayton 67), De Pena (Reach 79), Forshaw, Fabbrini, Garcia. Unused substitutes: Agazzi, Gibson, Downing, Nugent.
Wolverhampton: Ikeme, Doherty, Deslandes, Ebanks-Landell, Iorfa, McDonald, Saville (Henry 81), Price, van La Parra (Le Fondre 60), Wallace, Enobakhare (Afobe 60). Unused substitutes: Golbourne, Rowe, Ojo, Martinez.
Referee: K Wright (Cambridgeshire).