Beauvilier scored the game-winning goal early in the fourth period. Noah Dobson and Josh Bailey also scored for the Islanders (12-8-0), who took advantage of 30 saves by Ilya Sorokin.
John Tavares and Auston Matthews provided the answer in the Maple Leafs field (10-5-5). Erik Kallgren made 21 saves in his fifth overtime loss this season.
Mitch Marner added an assist to extend his streak to 13 games with one point. He scored 3 goals and 15 assists during this period.
The Oilers pay the price for the Devils
Captain Nico Hischier provided three assists and the Devils won their 13th straight game as they beat the Edmonton Oilers 5-2 in New Jersey.
The Devils thus matched a team record set during the 2000-2001 season. During the current streak, they have outscored their rivals 56-24.
New Jersey representatives will have an opportunity to hit the mark at home Wednesday against the Maple Leafs.
Yegor Sharangovich scored a sixth goal and ran a red light in the third game in a row. Jesper Bratt, Dawson Mercer, Damon Severson and Tomas Tatar were the other scorers for the Devils. Jack Hughes was an accomplice in two goals.
Vitek Vanecek made 27 saves for the Devils, who have not been defeated since October 24. Leon Draisaitl and Ryan Nugent-Hopkins have pulled strings in a losing cause.
Stuart Skinner blocked 23 shots for the Oilers, who visit the Islanders on Wednesday and the Rangers on Saturday.
The Flames inflict the Flyers seventh consecutive defeat
Blake Coleman had a goal and two assists to help the Calgary Flames win 5-2 over the Flyers in Philadelphia.
The three-pointer featured in first period hits by Jonathan Huberdeau and Dillon Dube, before scoring into an empty net in his 400th NHL game.
Rasmus Andersson and Trevor Lewis also scored for the Flames, while Jacob Markstrom made 23 saves. He was beaten by Joel Farabee and Tanner Laczynski, the latter getting the first goal of his career.
Travis Konecny missed a second straight game with an upper body injury. He has been the Flyers’ leading scorer and pointer since the start of the season.
Carter Hart blocked 24 shots for the Flyers, who lost their seventh straight game. They had lowered their flag to the Montreal Canadiens on Saturday after a shooting at the Bell Center.
The Flames were playing their third game in a six-game road. The Pittsburgh Penguins, Washington Capitals and Carolina Hurricanes will host them before their return to Calgary.
The Albertans will then play at home five times in a row, including one game against the Habs on Dec. 1.