Mathew Barzal beat Georgiev blocker side on a breakaway at 16:22 to make it 2-0. Barzal has scored in consecutive games after 12 straight without a goal.
"As much as you want to get on the score sheet, now that we're in and we know we're going to the playoffs, it's about playing the right way, trying to play playoff hockey the next five (games) here," Barzal said. "It's going to come quick. Before you know it we're going to be in Game 1."
Beauvillier scored again from the right circle with a low wrist shot inside the left post at 1:02 of the second period to extend the lead to 3-0.
Varlamov made 18 saves after the goal to complete the shutout.
"I'm really happy for 'Varly,' because Varly is as low-maintenance a goalie as we've ever had, and we've had some low-maintenance goaltenders, a few of them," Trotz said. "I'm really happy for Varly, but Varly will tell you it's a team thing. It says a lot about our team. I think that's our 10th shutout as a group, and that's a pretty good number."
NOTES: The Rangers played without forwards Chris Kreider (lower body) and Brett Howden (foot), and defensemen Ryan Lindgren (upper body) and Jacob Trouba (upper body). Kreider missed his second straight game, Lindgren missed his first of the season, and Trouba missed his sixth straight. Each is considered day to day. Howden, who was injured in a 4-0 loss to the Islanders on Thursday, is out for the remainder of the season. … Forward Morgan Barron made his NHL debut with the Rangers after being recalled from Hartford of the American Hockey League on Friday. He had one hit and was minus-1 in 11:56. … Islanders forward Jean-Gabriel Pageau didn't play the final 16:41 after going to the locker room following his only shift in the third period. He returned to the bench late in the period and Trotz said if the game was closer he could have played.