Ashley Battle added nine points to help the Liberty improve to 3-0 for the second time in their 11-year history. New York got off to a 7-0 start during the WNBA's inaugural season in 1997.
Seimone Augustus scored 18 points for the Lynx (0-6), off to the worst start in the franchise's nine-year history. Minnesota has lost its past nine games dating to last season.
Lindsey Harding added 14 points for the Lynx, losers of 14 of 15 going back to last year.
New York, which hadn't played in eight days, led nearly the entire way.
After Augustus made two free throws to give the Lynx a 9-8 lead, the Liberty went on a 15-0 run. Kraayeveld and Thorn each hit a 3-pointer in the spurt.
Harding made two free throws at the end of the third quarter to trim New York's lead to 50-45, but that was the closest Minnesota got the rest of the way.
The Liberty scored the first eight points of the fourth quarter, capped by Kraayeveld's 3-pointer, and cruised the remainder of the game.
Janel McCarville, a former standout at the University of Minnesota, had two rebounds in 6 minutes for New York.