The Portuguese coach made recovering Alli’s form of old one of his top priorities when taking over from Mauricio Pochettino last week and it is already paying dividends as the England international has now scored three times in three games under Mourinho.
Moussa Sissoko scored his first goal for over two years in emphatic fashion on the volley from Son Heung-min’s cross to make it 3-0 before two goals from substitute Harry Wilson gave Bournemouth late hope of a dramatic comeback.
Spurs first back-to-back league wins of the season moves last season’s Champions League finalists up to fifth and to within six points of the top four after Chelsea and Manchester City slipped up against West Ham and Newcastle respectively on Saturday.
Despite winning Mourinho’s first three games in charge, Spurs have conceded twice in every match and their defensive deficiencies were clear to see again early on as Bournemouth cut through the hosts’ midfield with ease.
Paulo Gazzaniga spilled Arnaut Danjuma Groeneveld’s driven shot with a save that did not inspire confidence in Hugo Lloris’s stand-in and the Argentine also failed to hold Diego Rico’s long-range effort moments later.
However, Mourinho’s risk in exposing his midfield with Alli playing so high just behind Harry Kane has also reaped plenty of reward in his first two weeks in charge.
The two combined to send Son scampering clear on goal with a rapid counter-attack, but the South Korean dragged his shot just wide.
Son was more accurate with his next involvement as he was picked out perfectly by Toby Alderweireld’s pass in behind the Bournemouth defence and his cushioned touch left Alli with the simple task of tapping home his first goal of the match.
Spurs then clicked into gear as Kane’s fiercely struck near-post shot was parried by Aaron Ramsdale, before Davinson Sanchez fired home only to be penalised for handling the ball as he controlled Sissoko’s shot.
Tottenham struck the knockout blow five minutes into the second half when another pinpoint long ball from Alderweireld was cushioned by Alli on his chest before he sat Ramsdale down and dinked the ball over the advancing goalkeeper.
That was Alli’s fifth goal in his last nine games after a 21-match streak between January and October without one for club and country.
And he should have had a hat-trick before the hour mark as Serge Aurier’s cross found its way through to him unmarked at the back post, but this time Alli’s curling finish was too high.
Spurs’ third was the pick of the bunch as Son burst down the left and picked out Sissoko in the middle for the Frenchman to smash on the volley back across Ramsdale into the far corner.
A first clean sheet of his reign would have rounded off a perfect day for Mourinho, but the Spurs defence was breached 17 minutes from time when set-piece specialist Wilson curled in a brilliant free-kick.
Wilson struck again deep into stoppage time to set up a grandstand finish and Jan Vertonghen needed to make a last-ditch challenge to deny Callum Wilson an equaliser with the final attack of the game.