The Avalanche captured the National Hockey League’s best-of-seven championship series four games to two for Colorado’s third NHL crown after 1996 and 2001.
“It feels like disbelief,” MacKinnon said.
“It’s hard to describe. To see all these warriors battle, it’s unbelievable. Words can’t describe what I feel right now.”
With the emotional road triumph, the Avalanche denied the Lightning a third consecutive title and fourth overall.
Colorado defenceman Cale Makar was named the winner of the Conn Smythe Trophy as the Most Valuable Player of the Stanley Cup playoffs.
Tampa Bay captain Steven Stamkos opened the scoring 3:48 into the first period off an assist from Czech left wing Ondrej Palat.
It was the Canadian centre’s career-best 11th goal of the playoff run.
MacKinnon netted the equaliser 1:54 into the second period, an angled shot just inside the near post for his 13th goal of the playoffs.
The Avalanche seized the lead by the final margin with 7:32 remaining in the second period on a goal from Finnish left wing Artturi Lehkonen, his eighth of the post-season, off a pass from Canadian centre MacKinnon.
The Lightning pulled goaltender Andrei Vasilevskiy in the dying seconds for an extra attacker to try and score an equaliser, but could not stop the Avalanche from hoisting the Stanley Cup.
The only team in NHL history to trail 3-1 and rally to win the Stanley Cup Final, as the Lightning attempted to do, was the 1942 Toronto Maple Leafs.