Two second-half goals from Spanish duo Andrea Orlandi and David Lopez secured the Seagulls their first away win in five attempts that moved them up to fifth in the Championship table.
For Tony Mowbray's Boro, they are down to 10th after their sixth defeat in their last seven games - and lie eight points off the top six, and just six points off the bottom three.
The visitors were forced into two changes with Casper Ankergren and Andrew Crofts coming into the side in place of the injured Tomasz Kuszczak and Will Buckley.
Both goalkeepers had a chance to test their handling in the opening stages. David Lopez's deflected shot was comfortably held by Jason Steele before Smallwood's drilled effort was saved down low by Ankergen, who was making only his second Championship appearance of the season.
But the early action was not a sign of things to come, with neither of the out-of-form sides able to find any kind of rhythm.
A deflected shot by Scott McDonald that went wide of Ankergen's post and an Andrew Halliday effort from the left fizzed across the face of goal was the best either side could muster before the interval.
In the second half Dean Hammond went close to breaking the deadlock in the 50th minute after he was found in the area by Jose Ulloa's terrific pass but the midfielder was unable to steer his header on target.
Then the home side went close as Wayne Bridge gave the ball away and Boro broke quickly, with Merouane Zemmama releasing McDonald down the right but the Australian's effort flew over the crossbar.
But it was the visitors who eventually broke the deadlock. Hammond squared from the right for Orlandi, whose run into the area had gone unnoticed by the Boro defence, and the Spanish midfielder side-footed past Steele for his fifth league goal
of the campaign.
They had Gordon Greer to thank for preserving their lead as the defender made two vital blocks in as many minutes to deny McDonald and then Curtis Main from getting shots at goal.
Mowbray turned to his bench, with Sammy Ameobi, Josh McEachran and Mustapha Carayol all brought on, but his side's attacking left them open at the back, and Orlandi had the chance to add a second but could only fire wide from the edge of the area.
But in the 76th minute Gus Poyet's side sealed the victory as Lopez was sent clear by Liam Bridcutt and he lobbed the on-rushing Steele to ensure his side remained in the play-off places.