Curry poured in 31 points and Thompson added 29 points, marking the 42d time in their careers they have both scored at least 25 or more points in a game and the seventh time this season.
Derrick Rose led the Knicks (25-38) with 28 points and Kristaps Porzingis contributed 24 points and 15 rebounds.
The Warriors (51-11) avoided a three-game losing streak, something they haven't achieved in 293 straight games.
A brief 8-2 run sealed the win, putting Golden State ahead 110-101 with 1:09 left.
A pair of free throws from Thompson extended the Warriors lead to 96-83 with 9:04 to play, but the Knicks put together a 13-1 blitz shortly after to creep back to 97-96 with 5:56 remaining.
Curry scored 15 of the Warriors 35 third quarter points for an 84-76 Golden State lead.
Porzingis poured in 11 points in the second quarter, including a fade-away jumper with 1.8 seconds left that provided New York with a 50-49 edge at the break. Curry was only 4 of 13 in the first half and 2 of 8 from long distance.
The Knicks shot 63 percent in the second quarter (12 of 19).
The Warriors featured an 11-4 run to retake the lead at 42-38.
With primarily their second unit on the floor, the Knicks used a 15-0 burst to move ahead 34-31 with 6:13 left in the second. Porzingis, the only starter on the court, contributed seven of those points. The Warriors missed 10 shots in the sequence, including four 3-pointers.
Thompson delivered 14 points in the first quarter, helping the Warriors to a 29-18 lead. Curry was 2 of 8 from the floor, missing his four 3-pointers.
NOTES: Golden State G Stephen Curry moved into 10th place on the 3-point all-time list (1,833). ... The Warriors are in the midst of a five-game road trip, tied for their longest trip of the season. All five games are against Eastern Conference opponents. Golden State travels to Atlanta on Monday and Boston on Wednesday to conclude the swing. ... Golden State scored a season-low 87 points in the loss to Chicago on Thursday, ending a streak of 36 games scoring 100 or more points. ... The Knicks have lost 21 games by 10 points or under. ... F Matt Barnes made his first start as a Warrior since March 4, 2008, at Atlanta. He scored three points in 18 minutes.