JaMychal Green added 18 points and 13 rebounds, while Dillon Brooks and Jarell Martin added 17 points each to help Memphis win its second straight.
Kristaps Porzingis led the Knicks with 21 points, while Enes Kanter finished with 20, including 18 in the first half. Courtney Lee and Michael Beasley had 18 points each.
Memphis played without starting center Marc Gasol, who sat out with an illness.
The Knicks pulled within 102-99 with about 47 seconds left on a 3-pointer by Lee, but Evans converted three free throws, including one when Lee was called for a technical with 17.8 seconds left.
Memphis stretched its lead to 18 midway through the third quarter. It was still shooting 51 percent after three quarters but opened the fourth not scoring for almost four minutes.
