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, recalled duo Ashley Barnes and Andrew Crofts going close to opening the scoring, but former Real Madrid youngster Alonso pegged them back with a scorching long-range hit in the 20th minute.
The 22-year-old left-back was strongly linked with a move to Fiorentina during the January transfer window but has emerged as a key performer for boss Dougie Freedman in recent weeks.
David Ngog and Lee Chung-Yong might have allowed the Reebok Stadium a more comfortable afternoon, but all Brighton had to show for a late barrage was Barnes' red card for dissent deep into stoppage time.
Gus Poyet's side drop to seventh, one point behind a resurgent Nottingham Forest with Bolton two further back in eighth.
Chris Eagles was rewarded for his injury-time winner against Blackburn on Tuesday night with a start at the expense of Medo Kamara, Bolton's only change.
Leonardo Ulloa and Barnes paired up in attack for Brighton, as Poyet made five alterations to the XI that drew 0-0 at Bristol City in midweek.
Barnes flashed a header over the top in the ninth minute before Wanderers midfielder Darren Pratley illegally halted Vicente's surge forward.
From the resulting free-kick, David Lopez found Crofts unmarked and Bolton goalkeeper Andy Lonergan stretched to push his strike away from the top corner.
Further slack marking from a Lopez set-piece allowed Ulloa to head goalwards and, when Wanderers only partially cleared, Crofts' low effort went behind via Lonergan's boot and the base of the post.
It was, therefore, 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 for his third goal of the season.
He might have added a second in the 32nd minute, stooping to head wide from Jay Spearing's right-wing corner.
As the interval approached, a pair of half-chances fell to Ngog to double Bolton's advantage but the ex-Liverpool striker could not capitalise on a missed kick from Brighton defender Adam El-Abd or a venomous Alonso cross.
Brighton once again displayed the greater industry in the second-half's opening moments and Lopez sweetly caught a 20-yard volley that flew narrowly over.
Crofts then blazed high and wide at the back post from Ulloa's right-wing cross after Bolton centre-back Zat Knight got a crucial glancing touch.
Wanderers responded and a measured Alonso pass gave 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 Lonergan's palms from the edge of the box.
In the 78th minute, Ulloa should have done better from another dangerous Lopez delivery and, as the clock ticked down, substitute Andrea Orlandi cut in from the left to flash past the far post with Lonergan beaten.
Brighton's frantic late push proved fruitless and Barnes' red card compounded their woes.
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- Ashley Barnes