New York, who won their only NBA titles in 1970 and 1973, will face either defending champions Oklahoma City or San Antonio.
They are tied 2-2 in the Western Conference final.
Jalen Brunson and Mikal Bridges each added 15 points for New York, who improved to 12-2 in the playoffs.
The Knicks closed the first quarter with an 8-0 run and began the second with a 12-0 surge to grab a 50-26 lead.
Shamet made two three-pointers in the pivotal stretch while Brunson and Miles McBride each made a three-pointer as the Knicks seized command.
Another Shamet three-pointer gave the Knicks their largest first-half lead at 61-32 in the second quarter before the Cavs trimmed it to 68-49 at half-time.
New York overwhelmed the Cavs with fast-break scoring and solid defensive work, pulling away for good in the third quarter.
Donovan Mitchell led the Cavaliers with 31 points.