Stoudemire, the Knicks' biggest offseason addition, hit only four of 11 field goal attempts. He scored 32 points on Sunday when the Knicks beat Italian team Olimpia Milano 125-113.
Stoudemire was surprised by Minnesota's defense.
"We're not used to seeing that in preseason," he said. "We definitely committed too many fouls, something we talked about previously."
The Timberwolves also won their first European preseason tour game with a 111-92 victory against the Los Angeles Lakers on Monday.
Minnesota's Michael Beasley, who scored 21 points against the Lakers, had 13 against the Knicks.
"We got the flexibility, we got the draft choices and free agents we were looking at. We feel like we are on our way to building a high-caliber team," Timberwolves coach Kurt Rambis said. "We got off to a horrible start. We didn't play well at the beginning, that's a simple fact, and then we did a pretty good job starting with the second half.
Love said his team needs to cut out the mistakes.
"After halftime, we cut down on turnovers. We know we ended up with 30 plus (turnovers), which is atrocious to say the least," Love said. "We're going to have to clean that up. That's part of us being a very young team."
Knicks guard Wilson Chandler scored nine points to help his team to a 29-22 advantage at the end of the first quarter.
Minnesota got back into the game after Stoudemire missed a couple of shots and was replaced by Danilo Gallinari after committing his third foul.
Beasley's dunk off a rebound tied the game at 40-40, before Love put them ahead with a tip-in. Gallinari's 3-pointer then put the Knicks back in front.
The Knicks led 48-47 at halftime, with Stoudemire getting six points. Love had 11 and Randolph 10.
The Timberwolves took a 72-63 lead in the third quarter when Anthony Tolliver made both free throws after he had been fouled by France center Ronny Turiaf, who was playing in front of his home fans at Bercy indoor arena.
"We set up really well ... then we made too many fouls," Knicks coach Mike D'Antoni said. "But the energy is good."
AP Sports Writer Samuel Petrequin contributed to this report.