The win moved the Knicks into second place in the Eastern Conference, percentage points ahead of the Indiana Pacers.
The Celtics, who could face the Knicks in the first round of the playoffs, lost their fifth game in a row and remained in seventh.
The Celtics, playing their second consecutive game without Kevin Garnett, were led by Jeff Green with 19 points and Paul Pierce with 16.
But they committed 20 turnovers, while the Knicks, who average the fewest turnovers in the NBA, had just eight.
In Auburn Hills, Mich., Nikola Pekovic had 18 points and 11 rebounds to lead Minnesota to a rare road win.
The game matched one of the league’s worst home teams against one of the worst on the road.
The Pistons haven’t won at home since before the All-Star break, losing seven in a row , while Minnesota had lost 10 of its last 11 road games.
Reserve J.J. Barea matched a season-best with 21 points for Minnesota.
Luke Ridnour scored 15 and Ricky Rubio added 14 points and nine assists.
Greg Monroe had 11 points and 12 rebounds for Detroit, while point guard Jose Calderon scored 14 points but only had one assist.
PACERS: Indiana coach Frank Vogel says he’s hoping to get all four of his injured players back during a four-game road trip that begins tonight in Houston.
Indiana played Monday night without swingmen Danny Granger and Lance Stephenson, point guard George Hill and power forward David West.
Vogel says Stephenson (strained right hip flexor) probably will play Wednesday night and that West could play. West has missed the past five games with a sprained lower back but did some post-practice work Tuesday.
Granger, who has missed most of the season with patellar tendinitis in his left knee, and Hill (strained left groin) are more likely to miss at least one more game.