Mark Stone had the puck poked away from him by Morgan Rielly on a 2-on-1, but he quickly retrieved it and found the trailing Eichel, who deked to his backhand before lifting a shot past Joseph Woll.
Eichel's goal came after Tomas Hertl tied it 5-5 with seven seconds remaining in regulation. Hertl got position in the low slot and redirected Eichel's centering feed past the glove of Woll.
That goal came shortly after Vegas previously thought it had tied it on what would have been Pavel Dorofeyev's third goal of the game at 15:50. However, Toronto challenged the play for offside, and the call was reversed after a video review.
Eichel finished with a goal and three assists, Dorofeyev scored twice, and Stone had a goal and two assists for the Golden Knights (23-11-12), who have won six in a row, including 3-2 in overtime at the Los Angeles Kings on Wednesday. Adin Hill made 23 saves in his first game since Oct. 20 because of a lower-body injury.
William Nylander had a goal and an assist before leaving midway through the first period with a lower-body injury for the Maple Leafs (23-16-8), who were coming off a 6-1 loss at the Utah Mammoth on Tuesday. John Tavares had a goal and an assist, Auston Matthews scored, and Woll made 27 saves.
Rielly gave the Maple Leafs a 1-0 lead at 2:05 of the first period, roofing a shot over Hill's blocker from the left circle after Nylander won a battle with Keegan Kolesar along the right boards.
Nylander then extended the lead to 2-0 at 5:03. He kicked a centering pass from Matias Maccelli to his backhand in front and lifted a shot past the blocker of Hill.
Nylander, though, would exit the game at 8:48 of the first. He was playing in his fourth game after missing the previous six with a lower-body injury.
Dorofeyev cut it to 2-1 at 8:12 with a power-play goal, scoring with a one-timer from the right circle off a quick pass from Marner, who was at the point.
Matthews responded at 9:57, redirecting Jake McCabe's centering pass inside the far post to make it 3-1.
Kolesar made it 3-2 at 5:51 of the second period. He spun off Rielly in front and knocked in the rebound of Braeden Bowman's shot.
Tavares pushed it to 4-2 at 12:46 when Maccelli's one-timer from the left circle deflected in off his stick at the post for a power-play goal.
Dorofeyev got the Golden Knights to within 4-3 at 2:10 of the third period. He scored his second power-play goal of the game from below the right circle after Marner's shot caromed to him off the end boards.
Scott Laughton put Toronto in front 5-3 at 8:58, taking a pass from Matthew Knies on a 2-on-1 and burying a one-timer from the right circle.
Stone made it 5-4 at 10:14. Ivan Barbashev's initial one-timer was stopped by Woll, but the goaltender's momentum carried him outside the crease, and on the ensuing scramble, Stone was able to knock it into the open net.
Stone has 17 points (nine goals, eight assists) during a 10-game point streak.
