The result sees Albion fall out of the npower Championship's top six, while Wanderers' late-season surge appears increasingly well timed as they made it eight matches without defeat.
Albion made most of the early running before former Real Madrid youngster Alonso fired a scorching long-range hit in the 20th minute.
All Brighton had to show for a late barrage was Ashley Barnes' red card for dissent deep into stoppage time.
It was against the run of play when the hosts burst up the other end to take a 20th-minute lead. There appeared to be little on as Alonso strode towards the left-hand corner of the area, but he unleashed a superb low drive across Thomasz Kuszczak and into the far corner.
Alonso might have added a second in the 32nd minute, stooping to head wide from Jay Spearing's right-wing corner.
Brighton once again displayed the greater industry in the second-half's opening moments and David Lopez sweetly caught a 20-yard volley that flew narrowly over.
Andrew Crofts then blazed high and wide at the back post from Leonardo Ulloa's right-wing cross after Bolton centre-back Zat Knight got a crucial glancing touch.
Wanderers responded and a measured Alonso pass gave David Ngog room to draw a fine stop from Kuszczak in the 55th minute.
A frantic melee ensued, with strangled shouts for handball coming as Matthew Upson got in the way of Lee Chung-Yong's shot, before a collection of Brighton bodies flung themselves towards Spearing's follow-up at the expense of a corner.
As the game entered its final quarter, Upson headed over from a corner and Vicente warmed Andy Lonergan's palms from the edge of the box. Sub Andrea Orlandi then cut in from the left to flash a shot past the far post with Lonergan beaten.
Brighton's frantic late push proved fruitless and Barnes' red card compounded their woes.