Sam Allardyce suffered his first defeat as Everton manager as an 88th-minute deflected strike from Ryan Fraser denied the Blues a point on the south coast.
The Toffees were hoping to extend their unbeaten run to nine matches but, having levelled through the fit-again Idrissa Gana Gueye just before the hour mark, were dealt a late blow when Fraser netted his second of the match when his shot hit the leg of Michael Keane and wrong-footed Jordan Pickford.
With the Blues in the middle of a gruelling Christmas schedule of four games in 10 days, manager Allardyce took the opportunity to freshen things up, making four changes to the side that started the goalless draw with West Bromwich Albion on Boxing Day.