Brighton needed just eight minutes to take the lead as Pascal Gross followed up after goalkeeper Zach Steffen had saved Solly March’s initial attempt.
However, Boro were back in it within five minutes when Jason Steele could only touch Chuba Akpom’s header from Ryan Giles’ cross on to the post and saw the ball ricochet in off him.
The Seagulls regained the lead with half an hour gone when Mitoma turned Solly March’s cross back across goal and Adam Lallana had the simplest of tasks to head home from point-blank range.
The top-flight side enjoyed the better of the possession as the whistle approached, but Boro continued to threaten on the counter as the half ended with Brighton leading 2-1.
Alexis Mac Allister got his chance as a half-time replacement for Lallana, and he made an impact within 13 minutes when he reacted smartly to flick full-back Pervis Estupinan’s shot past the helpless Zack Steffen and inside his left post to make it 3-1.
The Argentina star helped himself to a second with 10 minutes remaining when he turned Gross’ cross confidently past Steffen to make it 4-1.
It was soon five when another substitute, Deniz Undav, fired home with an excellent right footed finish after good work from March.
. MIDDLESBROUGH, ENGLAND - JANUARY 07: Alexis Mac Allister of Brighton & Hove Albion celebrates with teammate Tariq Lamptey after scoring the team's third goal during the Emirates FA Cup Third Round match between Middlesbrough and Brighton & Hove Albion at Riverside Stadium on January 07, 2023 in Middlesbrough, England. (Photo by Stu Forster/Getty Images)
Alexis Mac Allister of Brighton & Hove Albion celebrates with teammate Tariq Lamptey after scoring the team's third goal at Middlesbrough Photo: Stu Forster
. Jason Steele 7-10
Unlucky with the goal as the ball rebounded in off the back off his head. Made some vital saves in the first half as Middlesbrough continued to get in behind Albion. Comfortable in the second half Photo: Alex Burstow
. Tariq Lamptey 7-10
Very good performance from the former Chelsea man. Solid defending and always looking to get forward and supported March well Photo: NIGEL RODDIS
. Jan Paul Van Hecke - 8-10
Great to see Van Hecke get his chance in the first team. Looked comfortable in the first half and played the ball out from the back well. Read the game well. Photo: NIGEL RODDIS
1. Jason Steele 7-10
Unlucky with the goal as the ball rebounded in off the back off his head. Made some vital saves in the first half as Middlesbrough continued to get in behind Albion. Comfortable in the second half Photo: Alex Burstow
2. Tariq Lamptey 7-10
Very good performance from the former Chelsea man. Solid defending and always looking to get forward and supported March well Photo: NIGEL RODDIS
3. Jan Paul Van Hecke - 8-10
Great to see Van Hecke get his chance in the first team. Looked comfortable in the first half and played the ball out from the back well. Read the game well. Photo: NIGEL RODDIS
4. Levi Colwill - 7-10
An inexperienced central pairing and had a tough task against Chuka Akpom in the first half. Coped well and played better as game went on Photo: NIGEL RODDIS