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.
There was a welcome return for fit-again midfielder James McCarthy, who was handed his first Premier League start since the 6-3 victory against Bournemouth at Goodison in February.
Phil Jagielka, Aaron Lennon and Gana were also recalled to the starting XI, with Tom Davies, Mason Holgate, Yannick Bolasie and Ashley Williams dropping to the bench alongside Wayne Rooney, who was back in the squad having missed the previous two games through illness.
After a frenetic start, the first chance fell to Bournemouth when the industrious Fraser floated a free-kick towards the far post but Steve Cook, who was at full stretch, headed tamely wide of the target.
Then, Callum Wilson wriggled past Jagielka and Keane before firing in a low drive that was beaten away by the watchful Pickford.
Bournemouth were beginning to look menacing going forwards and Pickford had to be alert again to tip aside a snaking drive from Jordan Ibe after the former Liverpool man had turned sharply on the edge of the area.
In contrast, little was seen of Everton as an attacking force in the opening half hour, aside from a Dominic Calvert-Lewin header that flew harmlessly wide of Asmir Begovic’s left-hand post.
However, just as the Blues were threatening to grow into the game, a mistake from McCarthy led to Bournemouth breaking the deadlock in the 33rd minute.
The Republic of Ireland international’s stray pass back was intercepted by Wilson, who promptly fed Josh King on the right. The Norwegian’s pinpoint cross was emphatically volleyed past Pickford by Fraser, who was unmarked 10 yards out.
A similar mistake by Bournemouth defender Adam Smith almost presented Everton with an immediate equaliser.
Calvert-Lewin showed great awareness to seize onto the defender’s attempted back-pass, before cutting the ball back for Lennon but with the winger poised to pull the trigger, he was closed down by a covering defender.
Allardyce rang the changes at the beginning of the second half, introducing Rooney for McCarthy, and then Niasse for Calvert-Lewin, and both substitutes had a quick impact.
First, Rooney fired an early warning when he made a yard of space for himself on the edge of the area and drilled a low drive inches wide of the near post.
Then, Niasse played a pivotal role in Everton’s equaliser when it arrived in the 57th minute.
Gylfi Sigurdsson latched onto Cook’s mis-placed pass and fed Niasse, who had his back to goal on the edge of the box. The Senegal international then showed great vision, cleverly flicking the ball into the path of his compatriot Gana, who coolly guided a shot past Begovic with his right foot from 12 yards out.
Back came Bournemouth again and only a smart save from Pickford prevented the Cherries from regaining the lead, the England international diving brilliantly to his right to thwart Wilson, who looked a certain scorer when Simon Francis’ cross arrived at his feet.
A lively ending ensued as Ibe smacked the crossbar from the edge of the area, before a swift Blues counter-attack saw Niasse play in Sigurdsson from the left but the Iceland international took a touch and saw his effort blocked by Ake.
It looked like the moment Everton were going to grab all three points - and moments later they were left with nothing.
The winner arrived on 88 minutes in fortunate fashion for the home side as substitute Harry Arter cut a pass out left to Fraser. The 23-year-old took a touch and hit a low shot which took a wicked deflection off Keane, wrong-footed Pickford and ended up into the far right-hand corner.
It was tough luck on the Blues and enough to inflict a first defeat since Allardyce took over as manager at the start of December.