The Knicks were playing without Amare 88, on Monday.
Stoudemire was not with the team because of the death of his brother in a car accident in Florida and will be out for an unspecified amount of time, and Anthony suffered a strained right groin near the midpoint of the first quarter and did not return.
"I just have nothing but gratitude and thankfulness right now," said Lin. "This one was ugly and we lost a couple of players, but this team has a lot of will."
Al Jefferson paced the Jazz with 22 points as Utah dropped its third game in four tries.
New York held a 51-38 lead at the half, but the Jazz battled back in the third quarter and chipped away at the Knicks' lead.
Utah trailed by at least five points and by as much as 12 over the first eight minutes of the third, but after Jeffries' free throw put the Knicks ahead 70-63 with 3:51 left in the frame, the Jazz closed out the third with a 10-5 swing to get within two.
The Knicks' lead teetered between one and two possessions through the early portion of the fourth quarter before the Jazz went cold offensively in a nearly five-minute stretch that saw them score just two points.
Lin had five points in the 12-2 run that put New York up 92-80 with 4:18 left in the game and Utah never threatened again.
"It doesn't matter who we're playing or where we're playing at, we have to come out with a certain kind of attitude right from the beginning," Jazz head coach Tyrone Corbin said. "We have to play at a high level, especially on the defensive side of the floor, on the road for any chance to be successful and we didn't demonstrate that tonight."
The Jazz went 5-for-19 from the field in the fourth quarter, while New York shot 7-for-15 from the floor.
The teams traded buckets over the first three minutes of the game, but a Landry Fields driving layup sparked a 9-2 spurt by the Knicks to put them up 14-7 and they held a 19-16 lead after one.
An early 13-0 run put New York up by 15 five minutes into the second quarter and they held a double-digit lead for the remainder of the frame en route to a 51-38 halftime advantage.
New York improved to 6-7 at home this season, while Utah fell to 2-6 on the road...Utah outscored New York in the paint, 50-34...The Knicks' bench outscored Utah's 40-19...Raja Bell had 15 points and Gordon Hayward finished with 14 for the Jazz.