Marcus Tavernier opened the scoring for Bournemouth in the 25th minute with a goal directly from a corner kick while Junior Kroupi doubled Bournemouth's lead before half-time.
Nottingham Forest struggled to create significant chances throughout the match, despite having recently won a Europa League fixture.
Bournemouth fans chanted a chorus of “you’re getting sacked in the morning” at the new Forest boss after the club sacked Nuno Espirito Santo and Ange Postecoglou.
The game featured a heated midfield confrontation between Douglas Luiz and Justin Kluivert, resulting in both players receiving yellow cards.