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.