Pavel Dorofeyev and Ivan Barbashev also scored, and Mark Stone had two assists for the Golden Knights (26-16-14), who had lost seven of eight (1-5-2). Akira Schmid made 21 saves.
Elias Pettersson and P.O. Joseph scored, and Teddy Blueger had two assists for the Canucks (18-33-6), who have lost six of seven (1-5-1). Kevin Lankinen made 26 saves.
Eichel put Vegas ahead 1-0 at 5:09 of the second period. He slipped a shot by Lankinen after taking a pass from Rasmus Andersson from the half wall.
Cole Reinhardt scored 1:25 later to extend it to 2-0 at 6:34. Braeden Bowman found Reinhardt on the rush, who went backhand to forehand in front of Lankinen and finished at the far post.
Pettersson cut it to 2-1 at 7:11 after scoring on the rush, but Barbashev responded 28 seconds later to make it 3-1, roofing a wrist shot from slot off a drop pass from Stone.
Joseph cut it to 3-2 at 19:51 with a wrist shot from the left point.
Dorofeyev extended it to 4-2 at 2:31 of the third period after Mitch Marner won a puck battle near the side boards and found Dorofeyev at the far post for an easy tap-in.
Alexander Holtz scored a minute later to push it to 5-2, finishing from the low slot off a Keegan Kolesar rebound.