Ward popped up to equalise two minutes from time after Lewis Grabban's controversial first-half penalty had given Cherries a 14th-minute lead
Harry Arter and Marc Pugh returned to the starting line-up as boss Howe made two changes following Sunday’s 1-1 draw with Ipswich.
Arter, back after serving a one-match ban, replaced Josh McQuoid, while Pugh was preferred to Ryan Fraser who dropped to the bench.
As Brighton made most of the early running, Elliott Ward’s crucial last-ditch tackle prevented Leonardo Ulloa from taking aim after Adam El-Abd’s clearance had found him.
Lee Camp made a meal of saving a long-range effort from Andrew Crofts, the Cherries goalkeeping just about managing to help the ball on to the post.
Home players and supporters were incandescent with rage when referee Simon Hooper pointed to the spot after Pugh had gone down under Calderon’s challenge.
Grabban, however, made no mistake from the resultant penalty when he sent Seagulls goalkeeper Tomasz Kuszczak the wrong way to open the scoring.
As Brighton went in search of a quick response, Camp beat away a snapshot from Ulloa before Rohan Ince’s drive flew well wide.
Camp distinguished himself when he pulled off a top-drawer save to keep out Kazenga LuaLua’s fierce effort, the goalkeeper diving full length to his left to push the ball round the upright.
Cherries had a clearer penalty appeal waved away after Andrew Surman had been sent sprawling by Liam Bridcutt’s clumsy tackle after 30 minutes.
And on the stroke of half-time, Camp pulled another smart stop out of the bag when he pushed Ulloa’s lofted strike over the crossbar.
Kuszczak saved from Grabban after the striker had wriggled free at the start of the season half before the Seagulls went close to levelling in the 57th minute.
The lively LuaLua tried his luck with a rasping effort from 25 yards and, although Camp was finally beaten, the ball came crashing back off the crossbar.
A tame effort from substitute Ryan Fraser was comfortably gathered by Kuszczak before Camp palmed away Ashley Barnes’s header following a Kemy Agustien cross.
Kuszczak got down well to his left to parry Arter’s piledriver in the 86th minute before Brighton scrambled a late equaliser through Ward.
The defender’s header found its way through a crowd of players after Cherries had been undone by Ince’s hoisted free-kick to the far post.
Barnes almost snatched a winner for the hosts when his header clipped the crossbar, while Charlie Daniels saw his effort saved by Kuszczak following a swift break.
Cherries: Camp, Francis, Elphick, Ward, Daniels, O’Kane, Ritchie (Fraser, 71), Arter, Surman, Pugh, Grabban (Pitman, 82).
Unused subs: Addison, Harte, Rantie, MacDonald, Allsop (g/k).
Seagulls: Kuszczak, Calderon, El-Abd, Upson, Ward, Crofts (Agustien, 64), Lopez (Barnes, 72), Ince, LuaLua (Orlandi, 85), Bridcutt, Ulloa.
Unused subs: Andrews, Dunk, Chicksen, Brezovan (g/k).
Booked: El-Abd, Bridcutt.
Referee: Simon Hooper (Wiltshire).
Attendance: 28,282 (inc 1,668 away supporters).