Jack Quinn cut it to 5-1 at 5:12 of the third period on a wrist shot from the right circle, and Tuch pulled Buffalo within 5-2 at 8:01 from the bottom of the right circle to the far side.
Jeff Skinner made it 5-3 at 16:29 from the top of the left circle.
"I thought we still can take a little bit away from the third period, but we dug ourselves too big of a hole," Tuch said. "So, we have to go back to the drawing board and figure out what we did wrong at the start of the game."
O'Reilly scored into an empty net at 18:50 for the 6-3 final.
NOTES: Marner tied Pep Kelly (March 14, 1940, at the Montreal Canadiens), Babe Pratt (Dec. 17, 1942, at Montreal) and Borje Salming (Dec. 16, 1977, at the Minnesota North Stars) for the most assists in a road game in Toronto history. … Marner has 51 assists, reaching 50 in a season for the fourth time in his NHL career, the third-most in Maple Leafs history behind Darryl Sittler (six times) and Salming (five times). … O'Reilly (two goals, assist), Marner (three assists) and Tavares (goal, two assists) each had three points in the first period, marking the first time three Toronto players have done it. … The Maple Leafs scored their fastest four goals at the start of a road game since scoring four in 8:17 on Oct. 27, 1989, also at the Sabres. … Tuch's goal was the 100th of his NHL career in his 360th game.