Seagulls head coach Graham Potter made seven changes to the side beaten 2-1 at Tottenham on Boxing Day, with Lewis Dunk, Martin Montoya, Davy Propper, Yves Bissouma, Leandro Trossard, Jahanbakhsh and Neal Maupay all handed starts.
The Cherries made five alterations to the team which drew 1-1 with Arsenal, with Diego Rico, Harry Wilson, Philip Billing, Junior Stanislas and Dominic Solanke given recalls.
Within three minutes of kick-off the hosts were ahead, with Jahanbakhsh getting off the mark for Albion on his 27th appearance, firing home superbly after good set-up work from Aaron Mooy and Maupay.
Bournemouth responded with Joshua King forcing a decent save from home keeper Mat Ryan, while Mooy continued to impress at the heart of the Brighton midfield.
Chances then became hard to come by, however, as the game became scrappy and possession was given up too easily by both teams for much of the remainder of the first half.
The early part of the second half continued in the same vein as the closing stages of the first 45 minutes, with the hosts seemingly content to protect their one-goal advantage.
However, they thought they had gone one better than that when a Mooy free-kick into the area was only half-cleared and fell to Dan Burn, who turned and rifled home a fine finish, only for a VAR check to eventually rule the goal out for a marginal offside call.
The visitors responded to the reprieve by bringing on Callum Wilson and Ryan Fraser, but they had another escape soon after when Bissouma saw a low drive strike the foot of a post.
There was not to be another let-off, however, as 11 minutes from time the outstanding Mooy collected a pass from Trossard, turned past Chris Mepham and fired a fine finish into the top corner of the net to make sure of the victory.
Brighton 2-0 Bournemouth - Match Highlights