Boasting a 4-1 lead from the away first leg, Spurs were dominant again in the return fixture, a 4-0 success.
Not since 2011-2012, when coach of Real Madrid against APOEL, had Mourinho had a team score eight times over the course of a European knockout tie, and Alli was the star of the show.
Thursday's (AEDT) game at Tottenham Hotspur Stadium saw Alli make only his eighth start of the season - only one of which has come in the Premier League, in the opening-day defeat to Everton - but he made the most of his opportunity.
As well as executing a marvellous acrobatic volley - his first non-penalty goal of the campaign - at the end of a move he started, the England international provided two assists, doubling his seasonal tally.
This was the first time ever in a European match Alli had both a goal and an assist and the first time in any Tottenham fixture since December 2018.
These contributions and an impressive all-round display, including two shots, three key passes and 66 touches, suggest Alli is rediscovering his best form under Mourinho.
Since initially impressing when the Portuguese was appointed in 2019, Alli has fallen badly out of favour and was linked with a loan exit in January.
But Mourinho told BT Sport: "He had a difficult period. He had an injury, and at the same time he had an injury, it was the same period of talk, talk, talk about staying, leaving, leaving, staying.
"The market closed, the injury is gone, he started working with lots of motivation, and it's coming. That's what we need."
In his post-match news conference, the Spurs coach added: "The goal I don't need to speak [about] because everyone watched it and I believe around the world, on all these sports TV [channels], people are going to watch it.
"I don't need to talk about it. For me, the globality of the performance is what matters. He played very well. In every aspect of the game, he played very well.
"Of course he's not fresh, of course we can feel his performance, like in the first leg, from minute 55, 60 is going to go down - which is normal in the circumstances; injured, not training for a long time, come in for a couple of weeks.
"But in this moment where we are going to play every three days, 10 matches in March, to have Dele back at this level is amazing."
Substitute Gareth Bale was the beneficiary of one of Alli's assists, sweeping in a stunning third goal for his second of the tie.
Mourinho insists Tottenham's schedule means he does not need to have a first XI, but he acknowledged it would be hard to continue to leave Alli and Bale out of his league line-up.
"These are the headaches that I love," Mourinho said.
"The headaches I don't like are the headaches of selection [when] lots of people are not performing, lots of doubts, negative reasons. These are wonderful problems."
It was not just a night for Spurs' big names, though, as Dane Scarlett replaced Alli nine minutes from time and immediately teed up the fourth goal for Carlos Vinicius, also the scorer of the second.
Scarlett became the first 16-year-old to record a Europa League assist since Kylian Mbappe against Tottenham in December 2015.
Mourinho described the teenager as "a diamond" and said: "He has immense talent, very good physical development. He's very good, he's going to be very good.
"I hope that nothing is going to destroy that potential. He must have his feet on the ground and his head on his shoulders because he has fantastic talent."