Eddie Howe's side took just 18 minutes to break the deadlock at Bloomfield Road, with Matt Ritchie firing home a low drive from the edge of the box.
Callum Wilson added a second just before half-time with a close-range strike and Ritchie doubled his tally just before the hour.
Nathan Delfouneso came off the bench to pull one back for the hosts before Brett Pitman restored Bournemouth's three-goal advantage from the spot.
Marc Pugh extended the lead and Harry Arter capped of a fine afternoon for the south-coast club, who have now netted an impressive 17 goals in their last five league games.
Elsewhere at the top, Middlesbrough suffered a 2-0 defeat at fellow title rivals Ipswich Town, who climbed to second with a sixth win in nine games.
The Portman Road outfit are now one point ahead of Brentford, who emerged 3-2 winners in a thrilling game at Cardiff City, having been 3-0 up after 33 minutes.
Derby County missed the chance to go top earlier in the day by being held to a 2-2 draw at home to Norwich City, while Watford claimed a 1-0 win at Reading - where Steve Clarke took charge of his first game - and Blackburn Rovers beat Charlton Athletic 2-0 thanks to Jordan Rhodes' brace.
Fulham continued to climb the table after a 4-0 win at home to Sheffield Wednesday and Nottingham Forest were held 1-1 at home to Leeds United.
At the other end, crisis club Wigan Athletic slumped 2-1 at home to fellow strugglers Rotherham United, who had previously not won away since August.
The result means Wigan stay in the bottom three and have now only won once in their last 17 matches, leaving manager Malky Mackay with plenty to do to turn the club's fortunes around.
Ten-man Brighton remain in the relegation zone after Danny Batth's late equaliser cancelled out loanee Darren Bent's opener. Huddersfield Town became the latest team to be brushed aside by Gary Rowett's resurgent Birmingham City.
A wonderful 25-yard free-kick from David Cotterill was enough to seal the win for Birmingham, who have only lost once since the former Burton Albion manager took over.