Lauri Markkanen led the Jazz with 24 points. He had a layup followed by a tip shot with 5:20 left that got Utah to 115-108.
Grant and Anfernee Simons had back-to-back dunks to put Portland up 121-110 and the Blazers led comfortably the rest of the way.
When Lillard came to the free-throw line late in the game, the home crowd stood and chanted “MVP! “MVP!” Lillard hit both free throws to reach 60, but missed a jumper from distance with 29.1 seconds left that would have topped his career best 61.
He wasn't even aware he was near his career high until Blazers coach Chauncey Billups let him know after those free throws. Lillard thought he was coming out.
“Next time I came down they double-teamed me and I just rose up for three real quick and then they came down and scored," Lillard said. "There was still time on the clock, but I wasn’t going to be that thirsty to come back down with that much time in the game just to get a career high."
Lillard has four career games of 60 points or more. He's reached 61 twice.
Jazz coach Will Harvey was asked what Utah could have done to stop Lillard after double-teaming him for much of the game.
“I guess in theory we could have sent three people at him,” Harvey quipped.
After struggling for much of January, the Blazers were coming off a morale-boosting 147-127 victory over San Antonio on Monday.
Lillard finished 21 of 29 from the field, 9 of 15 on 3s and 9 of 10 at the line. He also had eight assists, seven rebounds and three steals.
During the third quarter Lillard scored 20 straight Portland points.
“You just kind of sit back and just enjoy it,” Blazers teammate Nassir Little said about watching Lillard reach 60. “Marvel at his greatness.”
Jazz: The quick trip to Portland was in the middle of two Jazz homestands. They played three in Utah before the game, then return for five games at home. ... Markkanen has made a 3-pointer in 37 straight games, the most for an NBA 7-footer.
Trail Blazers: It was the fourth game of a six-game homestand for the Blazers. ... Portland was hurt in the first half when starter Josh Hart left with a hamstring injury and did not return. Jusuf Nurkic left the game in the third quarter with left calf soreness and did not return. ... Lillard moved into sixth on the league's all-time 3pointers made list, passing Vince Carter.
Lillard is among just five NBA players with four or more 60-point games. Wilt Chamberlain leads the list with 32, followed by Kobe Bryant with six. Lillard, James Harden and Michael Jordan all have four.
“I ain't catching Wilt,” Lillard laughed.
Jazz: Host Dallas on Saturday night.
Trail Blazers: Host the Raptors on Saturday night.
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