Three-time NBA Most Valuable Player Jokic added 13 rebounds and 11 assists, shaking off a slow start that saw him score just six points in the first half to help the Nuggets pull away in a game tied 62-62 at halftime.
He needs just seven more playoff triple-doubles to surpass LeBron James (28) for second-most all time. Magic Johnson has the most with 30. Jokic also needs just two more triple-doubles to reach 222 (regular season + playoffs) to surpass Russell Westbrook (221) all-time.
Murray scored 17 of his 30 in the first half to keep the Nuggets close, finishing a perfect 16 of 16 from the free-throw line.
The third playoff series in four seasons between the teams got off to a physical start at Denver's Ball Arena, with more than 40 fouls called, a flagrant foul called on Minnesota's Jaden McDaniels, and a technical on Denver coach David Adelman.
The Nuggets trailed by as many as 12 in the first quarter before bearing down in the second period and pulling away after the break.
"I thought the second quarter was a much better defensive effort that really started trending into the second half," Adelman said.
Anthony Edwards led the Timberwolves with 22 points, and Rudy Gobert added a double-double of 17 points and 10 rebounds, but ultimately, they couldn't find an answer for Jokic.
"(Jokic) is such a patient player," Adelman said. "Early, it was a lot of our guys making plays for each other, and as they changed their coverages, then he went to work."
The Nuggets, who beat Minnesota in the 2023 playoffs on the way to the NBA title, then lost to them the following year, will try to double their advantage when they host game two of the best-of-seven Western Conference series on Monday.