The hosts raced into an early lead when Joao Pedro was fouled by Kepa Arrizabalaga in the box, and the Brazilian confidently converted from the resulting penalty.
Both sides threatened to find the net after Pedro's opener, as Antoine Semenyo sprinted away from the Brighton defence but shot straight at goalkeeper Bart Verbruggen, before Kaoru Mitoma hit the post at the other end in an entertaining first half.
The Cherries had to wait until the second half to get their equaliser, when a stunning strike from Justin Kluivert made it 1-1 and set up a fascinating final 30 minutes.
Substitute Danny Welbeck scored what proved to be the winner for the Seagulls, as the former Arsenal man netted just minutes after coming on for Pedro.
SPORTS MOLE'S VERDICT
Both sides are involved in the fight for European football next season, and Brighton have got a vital win here against the Cherries.
It was a game that could have gone either way, with both sides really going for it and showing that they want to be playing in Europe next season.
In the end, the experienced presence of Welbeck proved to be a masterstroke from Brighton boss Fabian Hurzeler, as he netted a crucial winner minutes after coming on.
The visitors can take some pride from their performance, however, as they demonstrated plenty of willingness to go forward and push for the result that they wanted.
Brighton's win moves them level on points with Bournemouth in the standings, as they both have 43 points each, with the Cherries ahead of them on goal difference.
BRIGHTON VS. BOURNEMOUTH HIGHLIGHTS
Joao Pedro goal vs. Bournemouth (12th min, Brighton 1-0 Bournemouth)
Brighton have the lead early on here! Having won the penalty himself, Pedro coolly steps up to the spot and sends Arrizabalaga the wrong way to give the hosts the lead after just 12 minutes.
Justin Kluivert goal vs. Brighton (61st min, Brighton 1-1 Bournemouth)
Wow. What a goal that is! Kluivert has curled an absolute beauty into the top corner to level this game! That is one that his father would have been proud of!
Danny Welbeck goal vs. Bournemouth (75th min, Brighton 2-1 Bournemouth)
Talk about making an impact from the bench. Welbeck has only been on the pitch for a matter of minutes and he may have scored the winner for the hosts!
Georginio Rutter played a lovely ball into him, and Welbeck takes a touch to compose himself before firing past the keeper to give Brighton the lead again!
MAN OF THE MATCH - JOAO PEDRO
A constant threat throughout the evening before being replaced by Welbeck, the Brazilian got Brighton going on the night, as he won and converted the penalty.
The former Watford man continues to be a problem for opposing teams, and he has now scored seven goals for the Seagulls this season.
BRIGHTON VS. BOURNEMOUTH MATCH STATS
Possession: Brighton 43%-57% Bournemouth
Shots: Brighton 11-19 Bournemouth
Shots on target: Brighton 4-5 Bournemouth
Corners: Brighton 1-9 Bournemouth
Fouls: Brighton 12-14 Bournemouth
BEST STATS
WHAT NEXT?
Both clubs are in cup action at the weekend, as Brighton make the long journey up to the North East to take on Newcastle United in the fifth round of the FA Cup.
Meanwhile, Bournemouth will return home to take on Wolverhampton Wanderers in the same competition, as the Cherries look to bounce back and progress to the quarter-finals.
Written by
Tom Humphrey