The Cherries had lost six of their previous seven top-flight matches but Brooks struck in each half - the second after Lewis Dunk was sent off for a second booking - to inflict a third successive defeat on Brighton.
Albion made three changes from their 2-1 defeat to Chelsea last weekend, with Yves Bissouma, Jurgen Locadia and Florin Andone coming into the starting line-up for Dale Stephens, Anthony Knockaert and Glenn Murray.
Bournemouth made five changes to their starting 11 after exiting the League Cup 1-0 away to Chelsea in midweek. Former Albion defender Steve Cook kept his place in the side as he remained an ever-present starter in the Cherries team this season.
Junior Stanislas fired a free kick over from the left-hand side of the penalty area in the early exchanges, before Albion threatened shortly afterwards.
Locadia drove forward down the left but his low centre was a fraction ahead of Florin Andone and Bissouma then fizzed a fierce effort just over from 20 yards.
Bissouma was a constant threat for Brighton and went close again on 11 minutes when he played a one-two with Pascal Gross but Asmir Begovic denied Albion's midfielder from close range.
Solly March sent a free kick over from 20 yards on 13 minutes, before Bournemouth had a spell of pressure themselves. Bernardo cleared Callum Wilson's cross as Stanislas waited to tap home and Albion keeper Mathew Ryan then pushed away Joshua King's shot moments later.
Brighton again soon threatened as Begovic produced a fine low save to keep out Locadia's low 20-yarder on 19 minutes.
The end-to-end nature of the game continued and Bournemouth took the lead on 21 minutes. Winger Brooks was allowed time to cut onto his left foot and drive a shot across Ryan and into the far corner from 20 yards for his fourth goal of the season.
Cherries midfielder Jefferson Lerma was booked for blocking Andone's charge forward on 31 minutes, before Bissouma had a shot blocked by team-mate Locadia six minutes before half-time.
Bournemouth made the brighter start to the second half and Stanislas curled a free kick inches wide from 25 yards.
Albion huffed and puffed going forward but failed to create any clear openings as their final ball often let them down, with several crosses going straight into the hands of Cherries keeper Begovic.
Lewis Dunk superbly cut out a lot Ryan Fraser cross to prevent Callum Wilson from tapping home but Albion's captain was sent off with 16 minutes to play for a second yellow card when he tripped Wilson.
The Cherries quickly added a second as sub Ryan Fraser sent in a cross from the left and Brooks looped a header over Ryan and into the far top corner.
Charlie Daniels looked to add a third but was denied by Ryan as Bournemouth collected just their second league win in eight attempts.
BOURNEMOUTH: Begovic; Francis, Cook, Ake, Daniels; Stanislas (Fraser 65), Lerma, Surman, Brooks; Wilson, King (Mousset 86). Subs: Boruc, Ibe, Defoe, Rico, Mings.
BRIGHTON: Ryan; Montoya, Balogun, Dunk, Bernardo; March, Bissouma, Propper, Locadia (Knockaert 69); Gross (Bong 76); Andone (Murray 80). Subs: Steele, Bruno, Stephens, Kayal.
HAVE YOU READ?