Randle and Reggie Bullock, who had 22 points, had four 3-pointers apiece in the first as New York put it away early. The Knicks stopped a three-game slide, returning to .500 at 25-25.
It was the largest margin of victory for the Knicks since 1996, a 125-79 win against expansion Toronto.
Randle was 1 for 7 from 3-point range during a 99-86 loss to Dallas on Friday, but was 5 of 9 from deep Saturday.
"I couldn't hit anything (Friday), so I guess the basketball gods turned it around," Randle said. "I just tried to come out and be aggressive, and really the whole team came out with energy."
RJ Barrett scored 14 points for New York, and Immanuel Quickley had 12. Elfrid Payton and Taj Gibson added 11 apiece.
Jerami Grant scored 16 points for Detroit, and Hamidou Diallo had 14.
Pistons rookie Killian Hayes returned after missing 41 games with a hip injury. The No. 7 pick out of France was scoreless in 20 minutes, grabbing five rebounds and dishing out three assists.
The Knicks opened the game with a 16-1 run. The Pistons got their first field goal when Diallo dunked an outlet pass from Hayes with 6:51 left in the first.
"I thought the unselfishness, the way in which we guarded and shared the ball, it got us off to a great start," Knicks coach Tom Thibodeau said. "I just loved the togetherness, the spirit of the team."
New York made nine 3-pointers before Saben Lee made Detroit's first in the second quarter.
The Knicks finished 17 of 36 (47.2%) on 3-pointers, outscoring the Pistons 51-24 from beyond the arc.
"They had more physicality, more want-to, they just outworked us," Pistons coach Dwane Casey said. "As a team we have to decide who we want to be. Are we a team of guys trying to get our numbers? I've got to coach better, I've got to get them ready and desperate, because we had none of the above tonight."
Knicks: C Norvel Pelle played after he signed a 10-day contract on Friday. In late action, Pelle scored a point, grabbed three rebounds and blocked two shots at the rim in the closing seconds, getting his new teammates off the bench in approval.
Pistons: Dennis Smith Jr. also returned after missing the last five games with a back injury. He scored five points in 12 minutes.
Hayes started the first seven games, but suffered a hip injury on Jan. 4 at Milwaukee. He played as a reserve Saturday.
"It's been a long time since I've been on the court, just being out there with my teammates," Hayes said. "It felt good to be back."
Derrick Rose scored seven points for the Knicks against his former team. Rose was playing in his second game back in Detroit since being traded by the Pistons in February for Smith and a second-round draft pick.
The Pistons followed their biggest win of the season Thursday with their most lopsided loss.
Detroit throttled Washington 120-91 to end a three-game losing streak, but Saturday was its worst loss of the season, surpassing a 118-91 loss to Golden State in January.
Knicks: At Brooklyn Nets on Monday.
Pistons: Open a five-game road trip at the Oklahoma City Thunder on Monday.
Randle outscores the Pistons by himself in the first quarter
Julius Randle has the hot hand in the first quarter, scoring 20 points and leading the Knicks to a 26-point lead.