Brooks fired Bournemouth ahead with a rasping shot from 20 metres in the 21st minute and, after Brighton had defender Lewis Dunk sent off in the second half, the 21-year old Welshman sealed the home side's win with a fine looping header.
Bournemouth, who celebrated only their second league win in the last eight matches, moved up to eighth on 26 points from 18 games while Brighton stayed 13th after suffering their third successive defeat.
Brooks, who joined the Cherries from Championship side Sheffield United during the close season after making his debut for Wales in November 2017, was praised by manager Eddie Howe after taking his league tally to five goals.
"Two great goals from David, both totally different but he showed his quality in both moments," Howe told the BBC.
"We've been pleasantly surprised, we knew we were getting a very technical and intelligent player. We liked him a lot from watching him at Sheffield United.
"He really buys into the team ethic and has a tactical understanding of how the team plays, and an ability to handle the Premier League and not get carried away with his early-season success."
Brighton had made a bright start and twice came close through Yves Bissouma, with Bournemouth keeper Asmir Begovic denying the Mali midfielder before he clawed out a stinging low shot by Jurgen Locadia.
Bournemouth took the lead when Brooks side-stepped his marker and unleashed an unstoppable shot into the bottom left corner of the net with visiting goalkeeper Matt Ryan clutching thin air.
Begovic kept out a Dunk header in the 44th minute and shortly after the centre back was dismissed for a second bookable foul Brooks was on target again in the 77th when he twisted in mid-air to head home Ryan Fraser's cross.
(Reporting by Zoran Milosavljevic; Editing by Ed Osmond and Clare Fallon)
Share
