David Pastrnak scored twice after Trent Frederic netted the first Boston goal, and Linus Ullmark stopped 20 of the 21 shots he faced as Boston won for the 16th time in its past 17 regular-season games. Arvid Soderblom made 30 saves for Chicago.
Bedard had a game-high six shots on goal in 21:44 of time on ice, though Boston finished with a 33-21 edge in that department.
With his goal, Bedard became the fourth-ever No. 1 overall pick, and first since Nathan MacKinnon in 2013-14, to record points in each of his first two career games as an 18-year-old. Bedard had an assist in a road loss to the Pittsburgh Penguins on Tuesday.
See a summary of the game at Flashscore
Canucks 8, Oilers 1
Brock Boeser scored four goals to lead Vancouver to a win against visiting Edmonton in the season opener for both teams.
Boeser tied the Vancouver record for goals in a game, producing the 12th such contest. J.T. Miller and Elias Pettersson each had a goal and three assists, Quinn Hughes added three assists and Thatcher Demko made 21 saves for Vancouver. Conor Garland and Dakota Joshua also scored as the Canucks matched their highest goal total ever in a season opener.
Leon Draisaitl scored for Edmonton. Oilers goalie Jack Campbell stopped 12 of 16 shots before he was replaced by Stuart Skinner, who finished with 12 saves and yielded four goals.
Maple Leafs 6, Canadiens 5 (SO)
Mitchell Marner scored the only goal in a shootout and Toronto came back from two goals down on two different occasions to defeat visiting Montreal.
Auston Matthews scored three goals for Toronto, including two late in the third period to tie the game. Noah Gregor and William Nylander also scored for the Maple Leafs. John Tavares added three assists, while John Klingberg had two.
Alex Newhook scored twice for Montreal. Jake Evans, Cole Caufield and Jesse Ylonen also scored for the Canadiens, with Kirby Dach adding two assists. Ilya Samsonov made 19 saves for Toronto, while Jake Allen stopped 37 shots for Montreal.
Hurricanes 5, Senators 3
Brady Skjei and Jaccob Slavin scored in a 3 1/2-minute span of the third period as Carolina pulled out a season-opening victory against Ottawa in Raleigh, N.C.
Skjei scored the goal-ahead tally with 12:09 to play in a wild third period. The teams combined for five goals in an 11-minute stretch of the final period, with each team posting one short-handed goal.
The Hurricanes also got goals from Michael Bunting, Teuvo Teravainen and Jordan Staal, while Frederik Andersen made 27 saves. Joonas Korpisalo stopped 37 shots for the Senators, whose goal-scorers were Mathieu Joseph, Parker Kelly and Tim Stutzle.
Avalanche 5, Kings 2
Mikko Rantanen had two goals and two assists, Nathan MacKinnon added a goal and two assists and visiting Colorado beat Los Angeles in the season opener for both clubs.
Cale Makar had a goal and an assist, Miles Wood also scored and Alexandar Georgiev turned away 34 shots for the Avalanche.
Carl Grundstrom and Quinton Byfield scored, while Cam Talbot made 30 saves for the Kings.
Flames 5, Jets 3
Elias Lindholm scored the late game-winner in a three-point game and Andrew Mangiapane collected two goals and one assist as host Calgary beat Winnipeg in the season opener for both teams.
MacKenzie Weegar and Rasmus Andersson also scored for the Flames, who won thanks in big part to a brilliant 34-save performance from Jacob Markstrom.
Kyle Connor, Alex Iafallo and Mark Scheifele scored for the Jets. Connor Hellebuyck made 17 saves.
