The New Zealand fly-half gave another master-class as Brave Lupus beat Saitama Wild Knights 24-20 in front of over 55,000 fans at Tokyo's National Stadium.
Mo'unga moved to Tokyo on a three-year deal after playing in his country's narrow Rugby World Cup final defeat to South Africa last year.
He won Super Rugby titles with Crusaders in each of the last seven years and he said he was "happy for others to experience" lifting a trophy.
"You have a vision at the start of the year -- you want to be the best in the competition," said the 30-year-old, who is not eligible to play for the All Blacks while he is in Japan.
"The work's still the same, and to finally be here, it's the same happiness, joy, a lot of relief."
Mo'unga was forced to endure a nervous end to a back-and-forth game when Saitama looked to have taken the lead with only a minute remaining.
Substitute Tomoki Osada crossed the line but a TMO review of the try revealed a forward pass in the build-up.
"One minute you're on the ground thinking you've lost the game, and then you see on the big screen that there might be a chance that there was a forward pass," said Mo'unga.
"That's just finals footy, that's the way finals happen."
'Rugby IQ'
Saitama were looking for their third title in four seasons but Tokyo took a deserved lead when Japan international winger Jone Naikabula scored tries either side of half-time.
Saitama, who were unbeaten during the league's regular season, came roaring back and took the lead after tries from Ben Gunter and Taiki Koyama.
Tokyo substitute Yuto Mori put his side back in front late in the game and they held on for the title despite Osada's late scare.
"The thing that was encouraging for us was 80 minutes -- that's all it can take for us to win a game, for us to change moments, and for us to be better than them," said Mo'unga.
"It came down really close but tonight we crowned ourselves champions and we're really proud."
Tokyo captain Michael Leitch said Mo'unga had made an "immense" contribution since joining the club.
"His decision-making, how he runs the week, how he controls the game and how he educates our players and staff," said the former Japan captain.
"He just brings another level of rugby IQ and I think that was evident today, just the way he managed the game and how he kicked and the options he took."
Loose forward Shannon Frizell, who also joined Tokyo after playing for the All Blacks at the World Cup, said the foundations for success had been laid before he and Mo'unga arrived.
"There's a lot of boys who work so hard behind the scenes," he said.
"We came in late. There's a culture that everyone who has come in buys into."
