Lafreniere scored on a breakaway set up by Trocheck and Panarin, getting a backhanded shot through Oettinger's five-hole at 11:24 to make it 3-0.
"They were dialed into the game," Rangers coach Peter Laviolette said of the line of Trocheck, Panarin and Lafreniere. "They created a lot of chances. They were on point."
Duchene started Dallas' comeback by cutting New York's lead to 3-1 at 12:57. He stayed onside at the left point and his pass attempt to Benn from the left circle went into the net off Urho Vaakanainen's stick.
Dadonov's power-play goal off a far post rebound of Mavrik Bourque's shot from the right circle made it 3-2 at 15:56.
The Stars outshot the Rangers 19-8 in the first.
"Not the start I dreamt about last night, but I just felt like once they got that third one, I felt like we were getting a lot of chances and if I could keep it there then we would be able to tie it up," Oettinger said. "We had a lot of chances early on. 'Quickie' made some good saves and we hit a couple posts. They were bearing down on all their chances. We felt like if we just kept playing that way we were going to get more and more chances. We had to step up and we did."
Robertson tied it 3-3 at 13:14 of the second period. He came from behind the net, around the left post and lifted a backhanded shot past Quick.
Trocheck gave New York the 4-3 lead at 12:56 of the third period with a power-play goal on a netfront deflection of Mika Zibanejad's shot from high between the circles.
Harley was in the penalty box at the time for a delay of game, puck over the glass penalty.
"It's not a good feeling," Harley said.
But a defensive zone turnover by K'Andre Miller, forced by Sam Steel's aggressive forecheck, led to Harley making it 4-4 with a shot from the right circle at 17:21.
"A lot better," Harley said. "Glad to see it went in. (Heck) of a job by Steel on the forecheck there and under the bar. All worked out."