Dele Alli, who looked like he was losing his way in the latter stages of Mauricio Pochettinos tenure, is a revitalised man and he scored twice as Spurs took a 3-0 lead.
Moussa Sissoko netted the third, his first for the club since September 2017, as Bournemouth looked down and out, but then old deficiencies began to show as the Cherries scored two at the end of the game.
On loan Liverpool forward Harry Wilson scored with an excellent free kick and grabbed his second in stoppage time, but it wasnt enough for Eddie Howes side.
Alli has been involved in two goals and one assist in his two Premier League games since Mourinho has taken the reigns and he looks to be a different player under the former Chelsea and Manchester United manager.
Playing from the back
Both of his goals were started by Toby Alderweireld, who hit a long ball to Son Heung-min who touched it on for the England international to score. Alderweireld was a more direct source for his second, as Alli controlled the defenders pass and flicked it around Bournemouth goalkeeper Aaron Ramsdale.
Son also got the assist for Sissoko with a close range finish as the South Korean continued his good start under Mourinho.
Tottenham are now up to fifth in the table but are six points behind Chelsea in fourth. The Blues dropped points against West Ham and opened the door ever so slightly for Spurs, who need to hold off the challenge from Wolves and Sheffield United behind them.
Bournemouth are now in 12th, but they are only two points away from Everton in 17th place and the Blades in 7th. Things are incredibly close in the Premier League at the moment and that makes every game a vital fixture.