Mourinho's glittering CV attracted him to Tottenham, with a side longing for tangible success turning to a proven victor for inspiration.
Shortly afterwards, Davinson Sanchez had a goal scrubbed off with VAR deciding he had handled in the build-up.
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.
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.
Mourinho is not naive to know there are some defensive difficulties to sort out in order to prevent leaking goals at the back if Spurs are going to challenge the top four. The winger pounced to score again in stoppage time to provoke some jitters on the home bench.
The Portuguese has won his two league games and a Champions League encounter since becoming the Tottenham manager earlier this month.
The Mourinho impact has been instant, with Alli rewarding his manager's faith by finding the net three times in three games.
"I can say we conceded four goals in three days at home but I prefer to say we scored seven goals at home in three days, which is fantastic".
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 global has now scored three times in three games under Mourinho.
"For me Dele is not a midfield player, he is a player to play like he is playing, close to Harry [Kane]".
Dele Alli has found his form since Mourinho stepped foot inside the club and asked Dele if it had been him or his brother playing - insinuating he hadn't been watching the real version of Dele out on the pitch. "I am pleased with the victory, the points and the goals", he said.
Bournemouth defender Stacey should have done far more to prevent Alli scoring a second goal, having also dropped off to play Son onside in the build-up to the hosts' opener.