After turgid first half, in which neither side ever looked like scoring, Boro captain Grant Leadbitter broke the deadlock 10 minutes after the restart with a superb free kick which left Wednesday goalkeeper Joe Wildsmith stranded.
The hosts were then reduced to 10 men when Daniel Ayala was shown a straight red card for a foul on Fernando Forestieri, however it didn’t affect the outcome after goals Alvaro Negredo and Marten De Roon sealed the win for Aitor Karanka’s side.
But who stood out for the Teessiders in this third-round tie? Here are the player ratings.
Goalkeeper and defence
Brad Guzan: 6 - Was rarely tested, even when Boro went down to 10 men. Collected a few crosses with ease.
Calum Chambers: 7 - Managed to get forward more in the second half from right back. Kept former Boro winger Adam Reach on the fringes.
Daniel Ayala: 6 - Was having a comfortable game until his red card midway through the second half. It looked harsh on first viewing.
Bernardo Espinosa: 7 - Read the game well, making a couple of important tackles and interceptions at the back.
George Friend: 6 - Solid in defence but was unable to provide his usual attacking prowess.
Midfield and attack
Adam Clayton: 6.5 - Replaced after 62 minutes. Protected the back four efficiently despite a limited threat from the visitors.
Grant Leadbitter: 8 - Led by example, organising and instructing in midfield. Brilliant free kick set Boro on their way.
Marten De Roon: 7 - A couple of loose passes in the first half, but showed plenty of energy throughout and earned his goal at the end.
Adama Traore: 5 - Subbed on 62 minutes. Tried to take players on most times he received the ball but few of his runs came off.
Cristhian Stuani: 6 - Quiet in the first half but gave Boro a threat on the break after the interval. Unlucky not to score the third goal after some neat footwork.
Alvaro Negredo: 6 - Was isolated upfront for most of the game and struggled to hold the ball up. Gambled for Boro’s second goal and was rewarded by Wildsmith’s error.
Stewart Downing: 6 - Gave Boro stability on the left after they were reduced to ten men.
Fabio: 6 - Slotted in well at right back after Ayala’s red card.