An early Harry Kane brace gave Spurs a first half advantage, before Christian Eriksen then concluded the scoring from close range in the second half.
Eddie Howe made just one change to his starting XI for the visit to White Hart Lane, as Harry Arter had recovered in time to partner Andrew Surman in the middle of the park and Dan Gosling dropped to the bench.
The hosts didn’t take long to show why they are challenging for the Barclays Premier League title. An early attack down the right flank saw Kyle Walker cross and Kane stroke the ball past Artur Boruc after just 44 seconds to make it 1-0.
Although the Cherries recovered well and created chances up the other end through Joshua King and Benik Afobe, Tottenham soon doubled their tally on the 15-minute mark.
Again it was Kane that did the damage, as the England striker raced onto a Dele Alli through ball and blasted a strike into the bottom right corner and past the outstretched Boruc.
Possession then started to level out, though Spurs looked a constant threat going forward. Eriksen showed his range of passing with a deep cross to Danny Rose at the back post, but the full-back thumped his strike into the side netting.
Before the interval the hosts almost made it three. Alli had the ball in the net after Kane flicked on Eric Dier’s deep cross, but the midfielder was denied by the linesman’s flag.
Moments later the Cherries almost gained a foothold back in the game. Max Gradel curled a 25-yard free-kick towards the Tottenham back post and Steve Cook rose to head, but the defender was unable to keep his effort down.
During the interval Eddie Howe made his first two changes of the afternoon. Arter and Afobe departed and were replaced in straight swaps by Eunan O’Kane and Lewis Grabban.
The Cherries created the first real chance of the second half, as King had a strike deflected behind for a corner after a well-worked set piece.
Not to be outdone, Tottenham soon threatened down the other end. Kane shrugged off Gradel to play in the marauding Walker, whose low strike skimmed past Boruc’s far post.
Then on 51 minutes the hosts eventually extended their advantage. Boruc parried a venomous Kane strike from distance, only for Eriksen to nip in and slot the rebound past the Polish stopper.
Eddie Howe then made his final change as Marc Pugh was called on to replace Gradel.
Tottenham were in confident mood and continued to dominate large spells of possession as the match drew to a close.
They also had chances to extend their lead, though Alli dragged his wide and Boruc got down well to deny the newly introduced Ryan Mason from close quarters.
Mauricio Pochettino then made his final change of the afternoon, as Nacer Chadli replaced Dier.
The Belgian was immediately involved in the action as he teed up Eriksen to strike from distance, but the midfielder rocketed the final strike of the game well clear over Boruc's crossbar.
Cherries XI: Boruc, Daniels, Cook, Francis, Smith, Ritchie, Arter (O’Kane, 45), Surman, Gradel (Pugh, 69), King, Afobe (Grabban, 45)
Not used: Federici, Gosling, Elphick, Distin
Spurs XI: Lloris, Walker, Rose, Alderweireld, Kane, Lamela (Carroll, 65), Dier Chadli, 89), Dembele, Alli (Mason, 81), Eriksen, Wimmer
Not used: Vorm, Son, Trippier, Walker-Peters
Yellow cards: Francis
Goals: Kane (1, 16), Eriksen (51)