Tottenham turned up the heat on with a convincing 4-0 victory over Watford at White Hart Lane to cut the gap to four points, but Antonio Conte's Blues saw out another win in the south coast sunshine to close in on the title.
An own goal from Adam Smith and a fine Eden Hazard solo strike put Chelsea in control within 20 minutes, but Joshua King's deflected strike handed Bournemouth hope going into half-time.
The Cherries grew in confidence, but Marcos Alonso made sure of the points with a stunning free-kick to keep Chelsea on course to finish top.
EPL | The Premier League table after 32 matches
Dele Alli, Eric Dier and a double from Heung-min Son saw Spurs sweep aside an injury-hit Watford side in the lunchtime kick-off.
Harry Kane made his return from injury in the comprehensive win as the England man was introduced in the second period, while Tottenham's goal difference now has a healthy look to it as the title race reaches its business end.
Liverpool have made life harder for Arsenal and Manchester United in the top-four battle as they fought back from a goal down to beat Stoke 2-1 at the bet365 Stadium, with Roberto Firmino and Philippe Coutinho scoring off the bench in the second half.
Manchester City kept up the fight for Champions League qualification as they beat Hull 3-1, while relegation rivals Middlesbrough and Burnley saw out a 0-0 draw at the Riverside Stadium. Elsewhere, Southampton beat West Brom 1-0 in the battle for a top-eight finish.