Boro took a first-half lead after an own goal from goalkeeper David Raya, yet Ivan Toney equalised for Brentford before half-time.
The Teessiders had chances to retake the lead but fell behind when Vitaly Janelt volleyed the ball home on 58 minutes.
Goals from Mathias Jensen and another from Toney then secured the points for Thomas Frank’s side who have now gone 20 league games without a defeat.
Boro handed a debut to new signing Neeskens Kebano who joined the club on a season-long loan from Fulham on transfer deadline day.
Yannick Bolasie also kept his place in the starting XI to make his home debut for the Teessiders.
Our writer Joe Nicholson has dished out his marks from the match – scroll down and flick through the pages to see them:
1. Jordan Archer - 6
Positioned himself well when the ball was played over the top. Beaten low down for both goals. 6 Photo: Alex Burstow
2. Djed Spence - 7
Managed to get forward more after the break. Was up against the lively Tariqe Fosu on the flank. 7 Photo: Getty Images
3. Nathan Wood - 7
Good in the air and comfortable on the ball in the heart of defence. 7 Photo: Bruce Rollinson
4. Marc Bola - 7
Captained the side and led by example at the back. Stepped out of defence to start the move which led to Boro’s goal. 7 Photo: Alex Burstow