Goals from Giovani Lo Celso and Erik Lamela proved enough for Tottenham to seal their place in round four despite a late wobble from the home side.
The two sides met after their 1-1 draw at the Riverside 10 days ago with the victors to face Southampton in the next round.
It didn’t take long for the hosts to lead this time around.
After a couple of nervy early touches from the Argentine, Giovani Lo Celso redeemed himself in style by intercepting a poor clearance from ‘Boro keeper Tomas Mejias before cutting inside and passing the ball calmly into the bottom corner.
Middlesbrough had a great chance to equalise not long after when loanee Lukas Nmecha raced through, selling Japhet Tanganga with a fake before forcing Paulo Gazzaniga into a fine low stop.
Chances are rued if not finished against top-tier opposition as Erik Lamela proved when he raced through on 16 minutes to make it 2-0.
Tottenham’s number 11 picked up the ball in a good position, drove at the defence and poked home a tidy finish for Spurs’ second of the night.
Ryan Sessegnon threatened to get in on the act when exchanging passes with Lamela, the England youth international eventually flashing a shot across the goal which was tipped wide.
Academy graduate Tanganga had a similar chance from the right side soon after but struck just wide much to the anguish of the Tottenham supporters keen to see ‘one of their own’ on the scoresheet.
Lucas Moura was close to finishing off a swift counter-attack before the interval but dragged his shot slightly wide as the score remained 2-0 to Tottenham at the break.
Jonathan Woodgate would have expected a response from his Middlesbrough side and they almost found a route back into the game when Lewis Wing’s low free-kick had Gazzaniga at full-stretch.
Boro were starting to grow into the game as the final 20 minutes arrived, the visitors looking to create chances from set-pieces.
The introduction of Heung-Min Son sparked some life into the tie but much of the second half felt like a formality for the home side as they seemed set to cruise into round four.
George Saville’s long-range effort almost secured a lifeline for Woodgate’s men with Christian Eriksen almost scoring at the other end with a cross-come-shot effort.
Then came the goal back. Saville latched onto a second ball before dribbling towards the area and firing a low effort past Gazzaniga to send his manager into frenzy as he frantically tried to relay instructions to his players.
Lo Celso and Dele Alli had chances to add to the scoreline late on as Spurs hung on to claim their place in round four of the FA Cup when they travel to Southampton.
Tottenham XI: Gazzaniga, Tanganga, Vertonghen, Sanchez, Sessegnon, Dier (Dele, 85′), Winks, Lo Celso, Eriksen, Lamela, Lucas (Son, 61′)
Tottenham unused substitutes: Vorm, Foyth, Cirkin, Aurier, Skipp
Middlesbrough XI: Mejias; Spence (Tavernier, 74′), Howson, McNair, Fry, Johnson, Clayton, Liddle (Saville, 57′), Wing, Nmecha (Gestede, 78′), Fletcher
Middlesbrough unused substitutes: Brynn, Wood, Malley, Roberts, Gestede
Attendance: 49,202
FA Cup
Tottenham Hotspur