Basil McRae's goal gave Minnesota a 6-2 lead at 1:23 of the third period before the Islanders came back.
Basil McRae and Mike Craig got the other Minnesota goals.
Lafreniere made it 2-0 at 6:20 when he picked up a rebound of Basil McRae's shot and fired it between Billington's legs.
The best exchange was with Basil McRae, in which they knocked each other down in rapid sequence.
In addition, Minnesota's Basil McRae was suspended for five games without pay.
Basil McRae, one of their enforcers, initiated the brawl by barging into Barrasso.
Most penalty minutes in a season: Basil McRae, 378 (1987-88)
In the first movie, it is Mike Modano and Basil McRae.
"Perhaps Basil McRae or Shane Churla would have scored a goal for us," he said.
He and Basil McRae were a formidable duo on the Minnesota North Stars at the end of the 1980s.