Howe's header with 16 minutes to go came as Brighton threatened to turn the match on its head after a red card just before the break for Bournemouth midfielder Marcus Browning.
The visitors, beginning life under caretaker-manager Stuart Murdoch following the departure of Sean O'Driscoll to Doncaster, were the better team in the first half.
Leon Best, on loan from Southampton, forced Brighton keeper Michels Kuipers into an early save with a fierce angled drive and it was no surprise when the Cherries took a 35th minute lead.
A pass by Shaun Cooper released James Hayter in behind the Brighton defence and he pulled the ball back for Steven Foley-Sheridan to fire into the roof of the net.
Bournemouth's good work in the opening 45 minutes was undone by Browning when he was sent off by referee Keith Hill for stamping on Brighton's 18-year-old midfielder Tommy Fraser.
It was the second time Browning had received his marching orders from Hill. He also saw red in an LDV Vans Trophy tie against Bristol City in 2003.
His departure handed the initiative to Brighton and they took full advantage.
Dean Hammond, captaining the team for the first time in the absence of Richard Carpenter, levelled on 53 minutes with an angled header from a Paul Reid cross.
Brighton were in front just seven minutes later when, in a goalmouth scramble from a corner, Gary Hart missed the chance to prod in Fraser's low cross but Alex Revell made no mistake from close range.
Brighton looked set for a second successive win under caretaker-manager Dean Wilkins but Bournemouth hit back.
Howe found enough room inside the area to head in a free-kick from Warren Cummings to earn the Cherries a point in Murdoch's first match in temporary control.