The Knicks, who broke a five-decade title drought in June but had lost their three opening games this season, overcame another slow start at Madison Square Garden to pull clear in the second half.
They avoided the ignominy of being the first reigning champions since 1969 to start the following season 0-4.
"We got to remember that Rome wasn't built in a day. This is a new year, new team," said last season's NBA Finals MVP Brunson, who added seven assists.
"Adversity started early, so we just got to fight back."
The Pistons - who had won their first three games of the season - started fast, going 13 points clear at the beginning of the second quarter thanks to free-scoring Paul Reed and Cade Cunningham.
Brunson struggled early, shooting just 1-for 9 in the first half.
But the Knicks pulled together for a remarkable rally, edging a single-point lead at halftime and roaring 25 points clear by the end of the third quarter.
They restricted the Pistons to a combined 25 points across the entire second and third quarters.
"I think we were just able to get stops, run a little bit, create a good enough lead, knowing that they were going to have a run in them to fight back," said Brunson.
With a home game against Charlotte looming Wednesday, and his team 21 points down, Detroit coach J.B. Bickerstaff emptied the bench with seven-and-a-half minutes remaining.
The Knicks' starters remained on court, and top-scorer Towns finished the night with 20 rebounds.
The Pistons, who finished with the best regular-season record in the NBA Eastern Conference last year, are now 3-1. Reed top-scored with 22, while Cunningham had 19 points, eight assists and nine rebounds.
Spurs down Kings, Celtics win thriller
Elsewhere, Victor Wembanyama helped the San Antonio Spurs to a 130-103 win over the Sacramento Kings with 29 points, 10 rebounds, five blocks and two steals.
The Spurs, who lost to the Knicks in last season's finals, had endured their own slow start to this campaign with two opening losses, but moved to 2-2.
San Antonio were rampant in a first half they led 80-54, with Wembanyama pouring in 23 points before the interval, and their lead barely dipped in a comfortable second half.
Julian Champagnie scored 26 points. The Kings sank to 0-4.
The Brooklyn Nets were also winless heading into action on Tuesday, taking on a loaded Boston Celtics team that haven't missed a beat despite changes, but in this one, the Nets forced Boston to earn every bit of this victory.
With Boston trailing by a single point at the very end of overtime, Jayson Tatum sank a game-winning buzzer-beater to ensure the Celtics won a thriller 125-124 against the winless Brooklyn Nets.
This was a very tense game from start to finish, with neither team managing to find a double-digit lead, ending 117-117 after regular time in arguably one of the most exciting games of the season to date.
Tatum scored 40 points plus eight assists, with Paul George adding 20 points as four of the Celtics' five starters had double digits on the night as they scraped and clawed to get the victory, moving to 3-1 on the season with their latest win.
In the late game, the Portland Trail Blazers topped their hosts, the Los Angeles Lakers, 136-129 to ensure they stay perfect in the West with a 3-0 record, while the Lakers have now lost one in four.
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