Dryden Hunt and Mika Zibanejad scored, and Alexandar Georgiev made 23 saves for the Rangers (36-16-5), who had a three-game winning streak end and are 8-3-1 in their past 11.
"I thought we did some good things, but I thought they were a little more desperate," New York forward Ryan Strome said. "… I think the first period was fairly even, they just had a little more desperation that accounted for those two goals, and then we did a good job getting back in the game and just a couple quick ones hurt us. Obviously, a tough result but [it's game No. 2 of] a four-game (road) trip, move on."
Hartman made it 1-0 at 10:38 of the first period through a screen for his fourth goal in his past four games. Joel Eriksson Ek increased the lead to 2-0 at 14:41, deflecting a one-timer from Foligno.
"I don't want to rate my game," Georgiev said after his fifth straight loss. "They've been frustrating. Just trying to [look at] every shot is a new experience for me, and just go from there."
Hunt got New York within 2-1 at 5:03 of the second period on a 2-on-1 with Strome for his first goal since Dec. 1, ending a 30-game drought. Zibanejad tied it 2-2 at 8:07 after taking the puck from Mats Zuccarello for a shorthanded goal.
Fiala gave Minnesota a 3-2 lead with a power-play goal at 9:13 after Matt Boldy swept the puck to him in the right circle for a wrist shot into an open net.
"That (third goal) was real tough," New York coach Gerard Gallant said. "We got that goal shorthanded, and I think it was the same power play that they scored, which is really tough. Usually, you get some momentum from that, and we lost our momentum there, and then the two breakaway goals were tough to handle, but that third goal was definitely tough."
Foligno made it 4-2 at 13:06 after splitting the Rangers defense and tucking the puck in on a backhand.
"It's just a little play where we kind of go out wide and cut in. I think [Matt Dumba's] hit me three times [with the pass] in preseason and I have not scored on it," Foligno said. "The 10th times a charm, I told him."