Johnsson gave the Devils a 2-1 lead on a snap shot from the left face-off circle at 1:47 of the second period.
Blackwood made a glove save on Travis Konecny's snap shot through a screen during a power play at 14:51 of the second.
Joel Farabee tied it 2-2 at 3:04 of the third period when he scored off a pass from Laughton at the left post following a turnover behind the Devils net.
"At the end of the day, you have plays you have to make, whether it's a checking play, stick play or a passing play," Flyers coach Alain Vigneault said. "Tonight, we tied it up and felt really good about where we were and, unfortunately, we didn't make the right plays."
Bratt scored on a 2-on-1 with Johnsson at 11:57 following a turnover at the Flyers blue line to give the Devils a 3-2 lead.
"[Bratt] did a great job screaming at me to let me know he was there, so I just had to put it on his stick," Johnsson said. "I knew he was going to score once he got it."
Nathan Bastian made it 4-2 when he scored on a wrist shot from the slot at 14:14 of the third. It was Bastian's second game with New Jersey since being claimed off waivers from the Seattle Kraken on Thursday; he played for the Devils the past two seasons before the Kraken selected him in the 2021 NHL Expansion Draft on July 21.
Johnsson scored into an empty net at 17:04 for the 5-2 final.
"Right from Day One in practice, I saw how good [Johnsson] was," said Hamilton, who is in his first season with the Devils. "He's just really smart and makes great plays, great at finishing. It's a lot of fun to play with him."
NOTES: The Flyers were 0-for-3 on the power play and are 4-for-50 (8.0 percent) in 16 games since starting the season 4-for-11 (36.4 percent) in their first four. … Max Willman, a forward recalled from Lehigh Valley of the American Hockey League on Saturday, had three shots, one hit and one blocked shot in 10:59 of ice time for Philadelphia. ... Bratt has scored six points (one goal, five assists) during a four-game point streak. ... Hamilton, who had a game-high 10 shots on goal in 19:43, used a custom stick in honor of his late friend Thea, a young girl with cancer he grew close with in Calgary. He said he intends to deliver the stick to Thea's parents. Hamilton played three seasons for the Calgary Flames (2015-18). … New Jersey is sixth in the eight-team Metropolitan, two points ahead of seventh-place Philadelphia.