With leading scorer Jalen Brunson sidelined with tightness in his right calf and Miles McBride also absent, Towns and Hart picked up the slack.
Towns added 21 rebounds and Hart scored 15 points with 14 rebounds and 12 assists and Mikal Bridges chipped in 27 points.
"Over the course of a season, whether it's injury, illness, foul trouble -- you need everybody," Knicks coach Tom Thibodeau said of the team's ability to keep the surge going despite being short-handed.
"As a team, if you prioritize winning and doing what's best for the group, that's what makes it enjoyable," he said. "You have everyone committed to each other. When you do that, good things come from that."
Collin Sexton and Jordan Clark scored 25 points apiece for Utah, but the Jazz suffered a fifth straight defeat.
In Detroit, the Pistons beat the Orlando Magic 105-96 but saw guard Jaden Ivey go down with what looked like a serious leg injury early in the fourth quarter.
Ivey collided with Magic guard Cole Anthony as they scrambled for a loose ball, Ivey collapsing to the court and holding his lower left leg.
He was eventually stretchered from the court.
"To see something like that -- it's devastating for the whole group," teammate Tobias Harris told NBA Network after the game. "Obviously, it's a big win for us, but after the game it's just the group coming together in prayer."
Ivey was enjoying an outstanding night, scoring 22 points to lead the way as all five Pistons starters scored in double figures.
Cade Cunningham scored 19 points with eight rebounds and nine assists. Jalen Duren scored 18 points and grabbed 11 rebounds and Harris scored 17 points for the Pistons, who never trailed.
Raptors snap skid
The Toronto Raptors, buoyed by the return of Immanuel Quickley, halted their 11-game losing streak with a 130-113 home victory over the Brooklyn Nets.
Scottie Barns scored 33 points and grabbed 13 rebounds and Quickly -- who missed 22 games with a torn elbow ligament -- added 21 points and 15 assists to help Toronto bounce back from a demoralizing 54-point loss to the Celtics in Boston on New Year's Eve.
Cameron Johnson scored 24 points to pace the Nets and D'Angelo Russell, newly arrived in a trade from the Los Angeles Lakers, added 22 off the bench.
In Washington, Jordan Poole returned from a two-game injury absence and scored 30 points to propel the Wizards to a 125-107 victory over the Chicago Bulls.
Poole connected on 10 of his 21 attempts from the field and drilled six of Washington's 17 three-pointers.
Justin Champagnie added 15 points and seven Wizards players scored in double figures in an encouraging performance for a team that notched just its sixth win of the season.
Chicago's Zach LaVine led all scorers with 32 points, but the Bulls were hampered by 20 turnovers leading to 33 Wizards points.
The Miami Heat, fueled by 32 points from Tyler Herro along with 23 points, nine rebounds and 10 assists from Bam Adebayo, led wire-to-wire in a 119-108 victory over the visiting New Orleans Pelicans.
Trey Murphy III scored 34 points to lead the Pelicans, who were playing with heavy hearts after at least 15 people were killed when a US army veteran drove a pickup truck into a crowd of New Year revelers in New Orleans early Wednesday in an attack authorities are investigating as an act of terrorism.
