Bournemouth 1 Brighton and Hove Albion 2
A resolute performance from Albion saw off the Cherries despite having only 10 men for the last half an hour.
Joao Pedro gave the Seagulls the lead inside four minutes. Great link-up play from Georginio Rutter and Danny Welbeck presented the Brazilian with little more than a toe in to give Brighton a 1-0 lead.
Bournemouth enjoyed plenty of possession and Evanilson forced a good save from Bart Verbruggen.
Evanilson did score for Bournemouth just before half-time but it was ruled out by VAR for offside.
Albion doubled their lead after a one-two exchange between between Mitoma and Pedro on 49 minutes, with the Japan international scoring from close range.
Ten minutes later Carlos Baleba was sent off for a second bookable offence and Albion were under the cosh.
It took until 93 minutes for Bournemouth to make a breakthrough when David Brookes toe-poked the Cherries back into it.
But it was too little too late for the hosts as Albion held on despite Antoine Semenyo smashing the bar in the last minute of added on time.
A first-half booking means that Semenyo will miss the visit by Bournemouth to Wolverhampton Wanderers next weekend. Lewis Cook was also shown a yellow card.
For Brighton, Rutter picked up a booking on the half hour as did Jan Paul van Hecke in added time.
Next up, the Seagulls host the Saints at the Amex. Brighton-born Russell Martin brings bottom-of-the-table Southampton to Falmer for an 8pm kick-off on Friday (29 November).