The Cherries had led since the 14th minute after Lewis Grabban converted from the penalty spot, but Ward nodded in a last-minute equaliser following a cross by Rohan Ince.
Victory would have given Eddie Howe's men a club-record third consecutive Sky Bet Championship away win - and the point means inconsistent Brighton keep in touch with the play-off hunting pack.
Andrew Crofts struck the post with a long-range drive in the opening 10 minutes and striker Leonardo Ulloa should have pulled the trigger when clean through on goal as the Seagulls made a positive start.
Oscar Garcia's men had won just two of their previous seven home matches and the Spanish boss had vowed that his players would start brightly to avoid another sluggish home display.
But it was the Cherries, who have now lost just one of their last six matches, who went ahead in the 14th minute courtesy of Grabban's coolly converted spot-kick.
Referee Simon Hooper sparked fury on the Brighton bench after pointing to the spot when Inigo Calderon appeared to win possession following a clean, last-ditch tackle on Marc Pugh.
Striker Grabban kept his nerve, however, and netted his 10th league goal of the season with an accurate finish into the bottom-right corner of Tomasz Kuszczak's goal.
Ulloa fluffed a clear opening to bring the Seagulls level in first-half added time following a pinpoint cross from Welsh midfielder Crofts.
Lee Camp, on loan from West Brom, sprung out of goal in an otherwise quiet half to deny the Argentinian frontman from six yards.
Liam Bridcutt, whose future at the Amex has been the subject of speculation following interest from Sunderland, offered another example of why his services are so sought after.
The 24-year-old was at his best, closing down opponents, spraying passes to the wings from the centre of midfield and providing energy and creativity to an otherwise lacklustre Brighton.
The Seagulls are hoping to mount another push for the play-offs following last season's semi-final defeat to Crystal Palace, but erratic home form, including defeat to league back-markers Barnsley last month has left them playing catch-up.
The Amex club have had particular difficulty breaking opponents down - and stubborn Bournemouth went close to doubling their advantage in the 48th minute when Grabban forced Kuszczak into a sprawling stop at the near post.
Kazenga LuaLua sent a 56th-minute rocket crashing onto the crossbar and Bridcutt shot wide as the Seagulls resorted to long-range efforts.
Garcia brought on attacking threats Kemy Agustien and Ashley Barnes in search of a leveller but hard-working Bournemouth, led by the energetic Grabban, snuffed out any openings the home side had.
Bournemouth's stern resistance eventually gave way, however, when Ward made a nuisance of himself in the box and headed past Camp following Ince's cross to grab the Seagulls a point.