Alex Scott handed Bournemouth the lead with a brilliant strike from outside the box inside the opening 20 minutes to give the hosts the half time lead.
But Brighton made a lively start to the second half and drew themselves level through Kaoru Mitoma, who headed home unchallenged three minutes after the resumption.
Cherries settled into the second half and retook the lead after 61 minutes, Antoine Semenyo converting from the penalty spot after Evanilson was brought down.
That was the final goal of the game as the Cherries won the three points to send them third in the league after four games.
Andoni Iraola made two enforced changes to the side which defeated Spurs before the break, both in defence as 18-year-old Veljko Milosavljevic made his debut in place of Bafode Diakite.
Veljko Milosavljevic made his Cherries debut_(Image: Richard Crease)_
James Hill came in for the injured Adam Smith at right back, while Lewis Cook returned from injury onto the bench and new signing Alex Jimenez was also named among the replacements.
The visitors were forced into a very early change as Jack Hinshelwood was forced off through injury after just three minutes, with Yasin Ayari coming on in his place.
There was little to threaten either goal in the opening 15 minutes, with neither side having an effort on goal.
But the Cherries took the lead with the first shot on goal of the game after 18 minutes.
Semenyo brought the ball down brilliantly just inside the box before passing to Scott on the edge of the area, the Englishman turning and finding the back of the net from the edge of the D.
Scott opened the scoring._(Image: Richard Crease)_
David Brooks saw a shot blocked in the box that prompted some appeals for a handball, before Evanilson headed a cross just over the bar.
Semenyo sliced a shot wide after taking on Ferdi Kadioglu, before Djordje Petrovic made a good save at his near post from a Yankuba Minteh effort.
Evanilson saw a header caught by Bart Verbruggen after some nice build up play on the left.
There were shouts for a penalty as the ball struck Lewis Dunk’s arm while the centre back was on the floor as the Brazilian looked to get a shot away, but nothing was given, as Bournemouth led at the break.
The first effort on goal of the second half went the way of the hosts, Brooks curling a free kick over the bar from around seven yards outside the box.
_(Image: Richard Crease)_
Brighton drew themselves level three minutes after the interval, as Mitoma headed home unchallenged from a Minteh cross from the right.
The visitors started the second half much the better side, as Minteh caused problems and had a shot turned behind by Senesi, before Danny Welbeck volleyed wide.
But Bournemouth retook the lead from the penalty spot, though, shortly after the hour mark.
Marcus Tavernier showed brilliant anticipation to cut out a pass at the back from Brighton and charged through at the retreating defence, passing to an open Evanilson who was brought down by Jan Paul van Hecke.
Semenyo scored from the spot_(Image: Richard Crease)_
Referee Peter Bankes pointed to the spot and Semenyo did the rest, sending Verbruggen diving to his right and slotting it just to the left of centre.
Iraola made a double change after 67 minutes, Justin Kluivert and Amine Adli replacing Brooks and Scott.
Adli’s first effort on goal came after 74 minutes as he curled a free kick towards the top corner, but Verbruggen got across to catch at the second attempt.
Minteh curled a shot towards the far post but Marcos Senesi was well placed to head the ball clear, before Kluivert saw a shot turned behind by van Hecke at the other end.
_(Image: Richard Crease)_
Hill headed straight at Verbruggen in his last act before he was replaced by Alex Jimenez for his debut, and Tavernier was replaced by Cook.
Semenyo cleared a Brighton corner off the line, with Evanilson replaced by Julio Soler as the game entered five added minutes, but Brighton weren’t able to equalise and the Cherries secured the points.
**AFC Bournemouth:** 1, Đ. Petrović; 3, A. Truffert; 5, M. Senesi (booked, 36’); 44, V. Milosavljević; 23, J. Hill (Jimenez 87’ (booked, 90+5’)); 8, A. Scott (Kluivert 67’); 12, T. Adams (booked, 45+5); 24, A. Semenyo; 16, M. Tavernier (Cook 86’); 7, D. Brooks (c)(booked, 31’)(Adli 67’); 9, Evanilson (Soler 90+1’).
**Brighton and Hove Albion:** 1, B. Verbruggen; 29, M. De Cuyper (Kadioglu 24’); 5, L. Dunk (c)(booked, 30’); 6, J. van Hecke; 34, J. Veltman; 13, J. Hinshelwood (Ayari 3’); 20, J. Milner (booked, 63’)(Baleba 66’ (booked, 73’)); 22, K. Mitoma; 10, G. Rutter (booked, 58’)(Gruda 67’); 11, Y. Minteh; 18, D. Welbeck (Tzimas 67’).