Two goals in three minutes from Mousa Dembele and Son Heung-min put the hosts in complete control inside 20 minutes and Harry Kane grabbed his 20th league goal of the season shortly after halftime as Spurs cut Chelsea's lead to four points.
Dembele struck after 16 minutes, slamming in a shot from six metres after Christian Eriksen's corner reached him at the far post through a crowd of players.
Son fired through the legs of keeper Artur Boruc after racing into the area from Kane's flick.
Kane, starting for the first time since injuring his ankle last month, wrapped up Tottenham's seventh successive league win after 48 minutes, turning Simon Francis all too easily and firing low past Boruc.
Substitute Vincent Janssen rounded off the action with a fourth goal in stoppage time, the Dutchman's first Premier League strike from open play since joining last year.
Bournemouth are seven points above the relegation zone before the later kickoffs and probably need one more victory to guarantee a third season of top-flight football.