AFC Bournemouth 1 Brighton & Hove Albion 3
Two quick first-half goals saw Albion through to the FA Cup 4th round.
Anthony Knockaert on 31 minutes and a first Seagulls goal for Yves Bissouma three minutes later gave the Seagulls a 2-0 lead at half time.
Marc Pugh pulled one back for the Cherries after good work by Andrew Surman 10 minutes into the second half.
But a Florin Andone strike just after the hour mark ensured the Seagulls remain unbeaten since the defeat at Bournemouth in the Premier League back in December.
Albion’s next match is against Premier League leaders Liverpool at the Amex next Saturday (12 January).