In the end, the Knicks scored a 90-83 victory despite playing without Carmelo Anthony and Tyson Chandler and with a hobbled Thomas.
"You never want to see anyone get injured, but injuries are part of the game," Thomas said. "When it happens you have to go out there and take advantage of the moment."
Thomas, who turned 40 last October, took advantage of his playing time by helping limit Utah's Al Jefferson and Paul Millsap to a combined 22 points on 8-for-21 shooing. They were not factors down the stretch, when New York held off the Jazz for its first victory in Utah since 2005.
"I gave him the game ball," coach Mike Woodson said. "I mean, he deserved it. He hadn't played  minutes maybe all year and we really didn't even know if he was going to play. ... It was a total team effort but he deserved the game ball tonight."
As a team, the Jazz shot only 38.2 percent, including 13-for-45 in the second half.
"We stayed home on their shooters," Thomas said. "They didn't get any wide-open looks. ... Myself and Kenyon [Martin] just competed and played solid defense" against Jefferson and Millsap.
Against Utah, the Knicks won for the first time on a four-game road trip.
"It was a great win for our ballclub," Woodson said. "To come to Utah, it's hard to win here. To play a good team that has played well at home and be short-handed like we are, we stepped up.
"Our defense really shined tonight, especially in the second half. ... Guys made offensive plays, but it was our defense that carried us."
J.R. Smith led the Knicks with 24 points, including four straight after Utah had taken a 60-56 lead midway through the third quarter.
The Knicks' comeback made Thomas' interaction with Utah's courtside fans even more enjoyable.
"I like communicating with the fans," he said. "It really helps me get going."