Brett Howden and Tomas Hertl also scored, and Mark Stone had two assists for the Golden Knights, who improved to 6-2-2 in their last 10 games. Carter Hart finished with 21 saves.
Mika Zibanejad and Alexis Lafreniere scored for the Rangers, who lost in overtime at home for the second straight day to fall to 3-8-3 at Madison Square Garden. Jonathan Quick had 26 saves.
After Hart denied Zibanejad to force a whistle in the Vegas end late in overtime, Eichel raced the other way following the ensuing face-off and beat Quick for his 12th goal and the win.
Hertl forced overtime with a tying goal with 52 seconds remaining in regulation.
Lafreniere gave New York a 2-1 lead at 13:01 of the second, firing a shot past Hart for his seventh goal.
Howden, a former Ranger, scored his fifth goal just 36 seconds into the game.
Zibanejad tied it at 9:08 of the second, tapping a loose puck past Hart for his team-leading 11th. Zibanejad has 261 goals as a Ranger, one behind Vic Hadfield for sixth place on the franchise list.
Stone has 20 points in 12 games this season.
Hart was playing his second game since returning to the NHL. The 27-year-old goalie was one of five 2018 Canada world junior hockey players acquitted of sexual assault in July. He made his first appearance for Vegas last Tuesday at home, a 4-3 shootout win over Chicago.
Golden Knights: Visit the New York Islanders on Tuesday night.
Rangers: Visit Chicago on Wednesday night.
Discover more from 6up.net
Subscribe to get the latest posts sent to your email.