Albion collapsed to their heaviest home defeat at the Amex.
Bournemouth's 5-0 romp at the Amex was compounded by a red card for Anthony Knockaert for an awful tackle.
Dan Gosling gave Bournemouth a first half lead.
Ryan Fraser doubled the Seagulls' deficit before Knockaert was sent-off for a crude challenge on Adam Smith.
David Brooks, Callum Wilson and sub Junior Stanislas added further goals for Bournemouth.
The Seagulls now face a crucial relegation showdown at home to Cardiff on Tuesday.
They remain five points above the Welshmen, who lost at Burnley.
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