With Tampa Bay trailing 2-1, Brandon Hagel pushed the puck past Buffalo goalie Devon Levi (21 saves) during a net-front scrum with seven seconds remaining in regulation for his second goal of the night and fourth of the season.
However, it didn't take long for Buffalo to answer via Cozens, who shot a wrister by Tampa Bay's Jonas Johansson (28 saves) for the Sabres' first win in three tries.
Zemgus Girgensons and Jeff Skinner also scored for the Sabres, who outshot the Lightning 31-23 and killed all four Lightning power plays.
Oilers 6, Predators 1
Leon Draisaitl scored twice in a four-point game and Zach Hyman collected one goal and three assists as visiting Edmonton defeated Nashville for their first victory of the season.
Ryan Nugent-Hopkins scored once and collected two assists, while Connor McDavid and Warren Foegele each tallied one goal and one assist for the high-octane Oilers.
Tommy Novak scored the lone goal for the Predators, who have lost two straight games. Goalie Juuse Saros stopped 7 of 11 shots before receiving a mercy pull following the first period. Kevin Lankinen made 17 saves in mop-up duty.
Flyers 2, Canucks 0
Sean Couturier scored his first goal in nearly two years and Egor Zamula also tallied to lift hosts Philadelphia past Vancouver.
Flyers goaltender Carter Hart stopped all 25 shots he faced en route to his sixth career shutout. Couturier converted a penalty shot in the first period. He missed one and a half seasons due to two back surgeries before returning at the start of this campaign.
Canucks goaltender Thatcher Demko made 40 saves.
Wild 5, Canadiens 2
Joel Eriksson Ek converted twice on the power play and Brandon Duhaime and Connor Dewar each scored a short-handed goal 25 seconds apart, lifting visiting Minnesota past Montreal.
Kirill Kaprizov scored a goal and set up two others and Mats Zuccarello notched three assists as the Wild improved to 15-1-0 in their past 16 meetings with the Canadiens.
Montreal's Alex Newhook capped the scoring by tallying with 2:25 remaining in the third period.
Islanders 1, Coyotes 0
Mathew Barzal scored a power-play goal 3:47 into the second period and Ilya Sorokin made 14 saves as New York shut down Arizona in Elmont, N.Y.
The Islanders improved to 2-0-0 for the first time since starting the 2014-15 season with four consecutive wins. New York opened the season with a 3-2 win over the visiting Sabres on Saturday.
Sorokin recorded his 17th career shutout in a mostly quiet night for Arizona's offence. Sorokin stopped three shots in the first period and three in the second, then eight more in the third when Arizona began getting some better scoring chances.
Kings 5, Jets 1
Trevor Moore had two goals and an assist as Los Angeles defeated hosts Winnipeg for their first win of the season.
Phillip Danault had a goal and two assists, while Arthur Kaliyev chipped in a goal and an assist for the Kings. Pierre-Luc Dubois also scored. Los Angeles goalie Cam Talbot stopped 26 shots.
Mark Scheifele ended Talbot's shutout bid with 1:16 remaining. Connor Hellebuyck finished with 24 saves for the Jets.
