They took the lead when Mousa Dembele finished off Christian Eriksen’s corner on 16 minutes.
Just three minutes later Son Heung-min doubled the lead from a narrow angle.
Harry Kane marked his return to the starting line-up with a goal just two minutes after the break, his 20th in the league this season.
Vincent Janssen added a late fourth shortly after coming on.
The win sends Spurs to within four points of leaders Chelsea and eight clear of Manchester City in third.
AFC Bournemouth are 15th, seven points clear of the relegation zone ahead of the other matches.