The Maple Leafs are off to a 2-0 start and spoiled Philadelphia's season opener one night after ruining Montreal's. Jonathan Bernier stopped 31 shots for the Maple Leafs.
Toronto acquired Bolland and Bernier in the offseason to bolster their bid to get out of the first round and make a run in the Eastern Conference playoffs.
Kessel scored his goal a day after he signed a $64 million, eight-year extension.
Brayden Schenn scored for the Flyers.
Bolland scored the go-ahead goal from the slot early in the third period. It was his first goal since the Game 6 clincher for the Chicago Blackhawks in the Stanley Cup finals.
He sealed this win with a power-play goal with 22.5 seconds left.
Kessel turned 26 on Wednesday with plenty of reasons to celebrate. He signed the whopping extension that will keep him off the free-agent market after the season.
A 20-goal scorer last season, Kessel knocked in a rebound late in the second for the tying goal.
Kessel helped make up for Toronto's lone second-period power play. The Maple Leafs came away empty because Flyers defenseman Nicklas Grossmann blocked three straight shots in 2 minutes to keep the game scoreless.
The Flyers wasted a fantastic chance to go ahead after Paul Ranger slashed Wayne Simmonds on a breakaway, setting up a penalty shot with 3.1 seconds left in the second period. Simmonds was easily stopped on his attempt to put the puck through Bernier's legs. Back on the bench, Simmonds slammed the boards in frustration.
Like Kessel, Bernier also is part of Toronto's long-term future. He signed a $5.8 million, two-year contract soon after he was acquired from Los Angeles. He was 29-20-6, with a 2.36 goals-against average and .912 save percentage as Jonathan Quick's backup with the Kings.
He kept Toronto in the game after the Flyers controlled the first period. Toronto went without a shot for a 12-minute stretch.
The Flyers took a 1-0 lead when Schenn pounded in Vinny Lecavalier's feed with 6.9 seconds left. Mark Streit also had an assist on the play, an early impact for two of Philadelphia's biggest offseason acquisitions.
The overhaul of an underachieving team that missed the playoffs for the first time since 2007 was in full force: Lecavalier, a former Tampa Bay captain, and Streit, a former Islanders captain, were signed, along with goalie Ray Emery.
Steve Mason won the opening night start over Emery. Mason, acquired in a late-season trade with Columbus, was given the start largely on the basis of a strong finish to 2013. Mason and Emery will likely share the job unless one gets hot and takes over.
NOTES: Toronto's Colton Orr received a minor penalty for a vicious cross-check to Flyers forward Jay Rosehill's face against the boards midway through the third. Orr retaliated after Rosehill checked Mark Fraser into the boards. ... Philadelphia and Toronto don't play each other again until March 8. ... The Flyers played their first game as members of the Metropolitan Division.