In their first game since trading forward Mats Zuccarello the Dallas Stars on Saturday, the Rangers scratched defenseman Adam McQuaid and forward Kevin Hayes with the 2019 NHL Trade Deadline on Monday at 3 p.m. ET. Each player can become an unrestricted free agent July 1.
"Listen, it's been an emotional 48, 72 hours for everybody and that felt really good, that goal," coach David Quinn said of Skjei's second goal.
The Rangers, 5-4-1 in their past 10 games, are 10 points behind the Carolina Hurricanes for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Kreider gave the Rangers a 1-0 lead 21 seconds in when he converted a cross-ice pass from Vesey on the rush.
Backstrom tied the score at 1 on a one-timer off a pass from John Carlson at 18:42 of the period.