The Blues have now lost two of their last three home games to West Ham United and now Bournemouth.
Earlier, leaders Liverpool put further daylight between themselves and the chasing pack with a 2-0 home victory over bottom-placed Watford.
Mohamed Salah was the hero of the day for Jurgen Klopp’s men as he followed his Champions League heroics in midweek with his eighth and ninth league goals of the season.
The Reds are now ten points clear at the top of the table, heading into their Club World Cup campaign next week.
At Brammal Lane, Sheffield United continued their impressive start to the season with a 2-0 win over relegation-threatened Aston Villa.
John Fleck scored both goals for Chris Wilder’s men as they moved up to fifth on the table, four points behind fourth-placed Chelsea.
Villa captain Jack Grealish failed to get the visitors back into the game as he missed a second half penalty.
Leicester City’s eight-game winning run came to an end at the King Power Stadium when second-from-bottom Norwich City took home a point following a 1-1 draw.
Teemu Pukki put the visitors ahead in the 26th minute but Norwich goalkeeper Tim Krul turned Jamie Vardy’s header from a corner into his own net seven minutes before halftime.
The Foxes remain in second place, seven points ahead of Manchester City in third.
Chris Wood scored the only goal of the game at Turf Moor as Burnley snapped a three-game losing run with a slim 1-0 victory over Steve Bruce’s Newcastle United.
