The 2-0 win in the sweltering Metropolitano Stadium delivered a first trophy in seven years for Liverpool, and -- finally -- a first win in seven finals for coach Jurgen Klopp.
The final whistle sparked wild scenes among the Liverpool fans in the stadium and back home in northwest England, where the team will have a victory parade on Sunday.
"We were all pretty much crying on the pitch, because it was so emotional, it was so big, it means so much to us," Klopp said.
For Liverpool it was sweet redemption after defeat to Real Madrid in last year's final in Kiev.
Mohamed Salah, who emphatically scored a penalty awarded in the very first minute, revealed he had drawn motivation from the disappointment of that match in which he left the pitch in tears with a shoulder injury.
"Before the game, I looked at a picture of last year and we were so disappointed to lose the final," Salah said.
"I was very disappointed after that injury, I went off after 30 minutes and we lost the game. It motivated me to win today. When you know how it feels to lose, you say to yourself 'Let's go and win that'."
- Guardiola's congratulations -
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Klopp revealed he had received a congratulatory call from Manchester City manager Pep Guardiola.
Three weeks ago, Liverpool were denied a first league title in 30 years by City, despite losing just once all season.
"We promised each other already that we will kick our butts next year again," Klopp said of his brief exchange with Guardiola.
"We will go for everything and we'll see if we get something."
Liverpool's sixth success in Europe's top club trophy -- coming after wins in 1977, 1978, 1981, 1984 and 2005 -- masks the fact they have not won the English title since 1990.
Centre-back Virgil van Dijk, named man of the match, said the team would try to put that right next season.
"In July when we start again, everyone starts on nil and everyone's working towards their goals," the Dutchman said.
"Obviously we want to challenge for every trophy if possible. We have the squad for it, but you've also seen it this year, you still have to do it, and hopefully we can challenge Manchester City again next season for the title."
Liverpool had won nothing since beating Cardiff City on penalties in the 2012 League Cup final.
After losing the Europa League final in 2016 and last year's Champions League final, Liverpool seized their chance.
Salah scored the penalty after Sadio Mane's attempted cross within seconds of the start struck Tottenham defender Moussa Sissoko and was adjudged to be handball.
Harry Kane and Son Heung-min laboured for Spurs but a match that never hit the heights was put to bed by a late strike from Origi, a forward who had played only a bit role for much of the season.
- 'Only the start' -
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Liverpool were already a club reborn under Klopp's management, but such a tangible reward was needed, three and a half years on from his arrival on Merseyside.
"I'm interested really in development, but I get it, we have to win things, and so it's really important that people don't ask now all the time about not winning things," Klopp said.
"Now we won something, and we will carry on, we want to win things, 100 percent.
"This is only the start for this group, it's a wonderful age group, they still have the best times in their career still ahead of them, so that's big."
Twelve months after two glaring errors by Loris Karius cost them dear against Real, his replacement Alisson showed just why Liverpool were prepared to pay £66.8 million (75 million euros, $84 million) to sign the Brazilian from Roma as he made several key saves late in the game.
"He of course played a sensational game, he looked completely unbeatable pretty much," said Klopp.
Van Dijk was again outstanding, snuffing out Kane's threat.
In Madrid, Liverpool fans who had swarmed into the city were overjoyed.
"Unbelievable, I can't believe we did it again. What a club. What a fan base. What a team. That's what we are all about," one supporter, 32-year-old Craig Williams, told AFP.