The victory came four days after the Cavaliers won at Chicago, which was their first of nine road games in 20 days.
"I want us not to have anything else on our minds until we finish all these road games," Coach Lenny Wilkens said after Thursday's game. "I'm always telling the players that these playoff races take care of themselves."
The Cavaliers (34-17) remain ahead of the Knicks (33-19) in the race for second place in the Eastern Conference. The two teams could meet in the second round of the playoffs, with the team finishing with the best record getting the homecourt advantage.
"We're not worried about what the Knicks and Bulls do," said Mark Price, who led the Cavaliers with 22 points. "We've got lots of road games left and it's a long season. You've got to win games on the road if you want to rise to the next level."
The Knicks led, 83-76, with 4:25 left, but the Cavaliers rallied to take a 90-89 lead on Nance's tip.
John Starks missed from the corner and Price's two free throws gave Cleveland a three-point lead. Mark Jackson's desperation three-point attempt from midcourt missed at the buzzer.
"I thought we had the game in hand, but we made some critical mistakes that cost us," Knick Coach Pat Riley said. "It wasn't because of lack of effort, or not playing smart. We just made some mistakes and a couple of turnovers and you can't do that against a team like that."
Daugherty had 19 points and 14 rebounds for Cleveland, 3-0 against New York this season.
Patrick Ewing finished with 26 points and 17 rebounds and Kiki Vandeweghe scored 17 points for the Knicks.
After the game, the Knicks announced they had picked up a backup center, 12-year veteran James Donaldson, in a trade with the Dallas Mavericks. The Knicks sent 6-foot-8 forward Brian Quinnett, 25, to Dallas.
Donaldson, who also played with Seattle and the Clippers, is averaging 6.2 points and 6.1 rebounds in 22.6 minutes this season, but saw his playing time reduced significantly in recent weeks.
Quinnett, a second-round draft pick in 1989, played in only 24 of the Knicks' 52 games this season.
"I'm numb about the whole thing," Quinnett said.
Houston 110, Philadelphia 101--Rudy Tomjanovich sat down in the wrong seat to start his first game as interim coach of the Rockets, but then moved over to the head coach's chair and directed the team to a victory at Houston.
Tomjanovich replaced Don Chaney, who was fired Tuesday.
Hakeem Olajuwon scored 23 points to lead the Rockets. Otis Thorpe scored 22 and Kenny Smith added 17.
Armon Gilliam led Philadelphia with 24 points and Charles Barkley, who wasn't traded as the deadline passed, added 23.
The Rockets, who led by 12 at halftime, were leading only 92-89 with 9:15 left to play when they went on a 9-1 run to take control.
"We anticipated they'd be ready at the top of the game," 76er Coach Jim Lynam said. "They were hot. I thought their defense was exceptional and aggressive."
Rice, who had 17 of his 30 points in the fourth quarter, missed a shot from the baseline. Teammate Grant Long got an offensive rebound and missed, but Rice tipped in the shot.
Rony Seikaly scored 20 points and had 14 rebounds for the Heat.
Miami, in its fourth NBA season, won its 25th game, one more than its total of last season.
Seikaly initially was given credit for the winning tip, but after a slow-motion videotape review, it was awarded to Rice. "Just call it a team tip," Seikaly said.