Dwayne Wade top-scored with 24 points while LeBron James registered 22 points, 11 assists and seven rebounds to notch his 27th consecutive regular season game with at least 20 points.
The hosts were outrebounded 52-24, the second-largest margin in team history, but the efforts of Wade and James ensured a one-sided night on the glass would not prove costly.
"I don't know how many times I've seen that, when you get doubled up on the rebounding and you still win. We'll take it," said Heat head coach Erik Spoelstra.
Minnesota led by six at the end of the first quarter, dominating the rebounds, but the Heat recovered to 52-49 at half-time, Mario Chalmers scoring a three-pointer with the final play.
Miami took control after the interval, dominating the turnover count - which yielded 25 points - and making 14 blocked shots and 12 steals.
"They were absolutely annihilating us on the glass," said Spoelstra.
"In the second half it felt we did a better job but they still had opportunities with second chance points.
"The only thing we could do at that point was put bodies on them and tip the ball away to somebody else."
Miami will look to make it three wins on the trot when they visit struggling Dallas on Thursday.