Albert Adomah opened the scoring in the 65th minute and then Danny Graham secured the points with Boro's second four minutes from time.
It might have been a different story if Brighton had made the most of the 78th-minute penalty they won, but Leonardo Ulloa missed that and the off-song Seagulls slumped to a third successive defeat before a crowd of 27,486 at the Amex Stadium.
Brighton, winners of only one of their previous five home games in all competitions, should have hit the target in only the fourth minute when Spanish midfielder David Lopez fired wastefully wide from a cross by Will Buckley.
Argentinian striker Ulloa, back in the Brighton side following a virus, then forced keeper Dimitrios Konstantopoulos to save after Lopez provided a pass.
The visitors responded and Seagulls keeper Tomasz Kuszczak was also called into action as he dived full length to save two-handed from Luke Williams, who cut in dangerously before unleashing a goal-bound shot.
Kuszczak did well again in the 18th minute by diving to his left to punch away a curling shot from Lee Tomlin.
There was more work for former Manchester United custodian Kuszczak to do when Boro skipper Grant Leadbitter got himself into a useful position but his low shot was taken smartly next to the post.
Konstantopoulos rose to claim an effort from Buckley before Leadbitter drove wide at the other end.
Boro were looking comfortable on the ball but Brighton threatened just before the break when both Ulloa and Jesse Lingard had shots charged down following a corner from substitute Jake Forster-Caskey, who had come on as a replacement for the injured Buckley.
Brighton, seeking their first home win over Boro for 24 years, started the second half in lively fashion and Lingard shot wide from a Stephen Ward back-heel before a Forster-Caskey drive was taken by Konstantopoulos.
Seagulls head coach Oscar Garcia made his second change when former Newcastle winger Kazenga LuaLua came on for Lopez and immediately showed blistering pace with a run down the left and a low cross that fizzed across the face of goal.
LuaLua did well again shortly after with a teasing low cross to the near post but Keith Andrews failed to hit the target.
The miss proved costly as Boro counter-attacked to take the lead through Adomah's 11th goal of the season on 66 minutes.
A mistake by Albion captain Gordon Greer allowed Graham to cross and Adomah had the easiest of tasks to steer the ball home from inside the six-yard box.
Brighton had an opportunity to pull level seven minutes later, Ulloa having a goal-bound header saved from six yards following an accurate cross from Bruno Saltor.
The Seagulls had an even better chance to get on terms soon after when they were awarded a spot-kick, but Ulloa blazed his effort over the bar.
Brighton's 12-goal top scorer stepped up to the spot after skipper Friend brought down substitute Solly March, but Ulloa's attempt was dreadful and the ball sailed harmlessly into the home fans behind the goal.
Graham then doubled Boro's lead, and in the process sealed the win, four minutes from time with a low shot from 12 yards following a pass by Leadbitter.