Jokic became the first player in history to lead the league in points in a single postseason.
Unable to shake the tenacious Heat or their own closing-night jitters, the Nuggets missed 20 of their first 22 3-pointers.
Trailing by three with 15 seconds left, Butler jacked up a 3, but missed it.
“Those last three or four minutes felt like a scene out of a movie,” Heat coach Erik Spoelstra said.
Denver is the home of the Larry O’Brien Trophy for the first time in the franchise’s 47 years in the league.
Until Butler went off, he was 2 for 13 for eight points.
The tone was set with 2:51 left in the first quarter, when Jokic got his second foul and joined Aaron Gordon on the bench.
True to the Nuggets’ personality, they kept pressing, came at their opponent in waves and figured out how to win a game that went against their type.
Over their near five-decade stay in the league, the Nuggets have been the epitome of a lovable NBA backbencher – at times entertaining, adorned by rainbows on their uniforms and headlined by colorful characters on the floor and bench.
Before this season, there were only two teams founded before 1980 – the Nuggets and Clippers – that had never been to an NBA Finals.