In his Toronto debut, Bernier (31 saves) was the difference, and the Flyers struggled on the power play (1 for 7).
"We had a lot of chances to go up by two goals and couldn't put one away," center Vinny Lecavalier said. "Give Bernier credit."
The Flyers lost even though they fired 73 shots (32 on goal), compared with Toronto's 42 (25 on goal).
Last season, the Flyers were one of the NHL's worst teams in even-strength situations. Toronto outscored them, 2-0, when the teams were five-on-five Wednesday.
Brayden Schenn, who (surprise, surprise) was on the top line with Claude Giroux and Scott Hartnell, gave the Flyers a 1-0 lead with a power-play goal late in the opening period.
Lecavalier skated behind the net and fed Schenn for a one-timer from the slot with 6.9 seconds left in the first period.
But Toronto, coming off a 4-3 win in Montreal on Tuesday, took advantage of a Max Talbot turnover to tie the score with 2:54 to go in the second period.
Defenseman Dion Phaneuf intercepted Talbot's pass at center ice, starting a possession in the Flyers' defensive zone that ended with Phil Kessel's putting a rebound past Steve Mason (22 saves).
With 3.1 seconds left in the second period, Flyers winger Wayne Simmonds was pulled down by defenseman Paul Ranger and awarded a penalty shot. Simmonds, trying to put his shot through the goalie's legs, was stopped by Bernier to keep the score tied.
"Bernier was really patient," Mason said. "When you make a big save at that time in the period, it's going to give your team momentum."
It was the first time the Flyers had a penalty shot attempted in their home opener since 1997, when Trent Klatt was stopped by John Vanbiesbrouck.
Simmonds, who faced Bernier numerous times in practice when they were Los Angeles teammates, blamed himself for the loss.
"I missed it; it would have been the difference in the game, I think," he said. "I wanted to get a quick shot and go five-hole, and obviously he read it."
For the Flyers, it was the start of what they hope will be the Great Redemption Season. They failed to make the playoffs in 2013 - starting the year 0-3 and 2-6, and not going over .500 until the final game - for just the second time in the last 18 seasons.
"It's been a long summer after not being happy with the results last year," Giroux, the team's second-year captain, said before the game. "Every day I think about it, and today is the day" to start fresh.
Midway through a Flyers-dominated first period, Giroux made a deft pass to streaking left winger Hartnell, who tipped the puck off the left post.
In franchise history, the Flyers are 21-18-7 in openers, including a 15-11-3 mark in seasons that started at home.