The Knicks learned earlier Saturday that Stoudemire will have right knee surgery that will sideline him approximately six weeks. But they still have plenty of scoring off the bench, with Steve Novak adding a season-high 20 points.
Alec Burks scored 14 points and Gordon Hayward had 13 for the Jazz, who completed a 0-4 road trip that dropped them into a tie with the Los Angeles Lakers for the eighth and final playoff spot in the Western Conference.
Utah played without starting forward Paul Millsap because of right knee inflammation.
The Knicks bounced back from a 95-94 loss to Oklahoma City on Thursday to win for the sixth time in eight games, seizing control with an 18-2 run in the second quarter and taking a 32-point lead in the second half.
They played their third straight game without Anthony, their leading scorer who they said has a stiff and sore right knee. Coach Mike Woodson said he remains day to day, so Anthony could return during the Knicks' five-game western trip that begins Monday at Golden State and includes a stop in Denver for what would be Anthony's first game there since the Nuggets traded him to New York in February, 2011.
Stoudemire will be gone much longer, just as he was playing well.
There was no indication there was anything wrong with the former All-Star, who had matched his season high of 22 points in back-to-back games this week. He then scored 16 points Thursday against the Thunder, but sat out the morning shootaround with what Woodson said was pain in both his knees.
Stoudemire then had an MRI exam and the Knicks announced before the game he would have a debridement, a procedure to remove tissue, within the week and would miss approximately six weeks. That could have him back for the playoffs, though he missed two months after having the same surgery on his left knee in the preseason.
He came back from that on New Year's Day and has averaged 14.2 points in 29 games off the bench.
Smith, who scored a season-high 36 points Thursday but missed the potential winning shot, made four 3-pointers and Novak was 5 of 10 behind the arc.
Raymond Felton finished with 15 points for the Knicks.
Utah's last three losses had come by a combined five points, falling 89-88 on Friday in Chicago on Marco Belinelli's late 3-pointer. But the Jazz were out of this one early in their seventh loss in eight games.
The Knicks led by two before Novak and Felton made 3-pointers in a 10-0 burst that made it 41-29. Al Jefferson made a hook shot, but Novak answered with consecutive 3-pointers before Pablo Prigioni sank a pair of free throws to make it 51-33 with 1:46 remaining in the half. The lead peaked at 55-36 on Tyson Chandler's dunk and the Knicks were up by 17 at the break.
It ballooned to 75-45 on a pair of free throws by Iman Shumpert with 4:15 left in the third and would eventually reach 32.
Chris Copeland scored 12 points in just seven minutes and Kenyon Martin, now likely to have a bigger role in the rotation, scored 10 as the Knicks' reserves, who came in third in the NBA with 40.3 points per game, totaled 75.