Pickard and MacKinnon are good friends, and they talked to each other throughout the game.
"We were kind of jawing at each other, all fun and games," said Pickard, who made 24 saves. "It's good to see him doing well. It was definitely a well-earned point for us."
Said MacKinnon: "It was fun. He's definitely a different goalie. He's loose in the net, he's always fun to talk to. He's a good buddy of mine and I definitely miss him here."
Alex Kerfoot and Mikko Rantanen also scored for the Avalanche (18-16-3), who are 1-1-0 in the first two of a six-game homestand. Semyon Varlamov made 31 saves.
James van Riemsdyk, Roman Polak and Matt Martin scored for the Maple Leafs (23-14-2), who have gone 2-1-1 in the first four of a five-game road trip.
Pickard was off for an extra skater when van Riemsdyk scored his 17th goal to tie the game 3-3 with 1:55 remaining in the third period.
"Anytime you can get a point, it's big," van Riemsdyk said. "Obviously, we'd like to get the second one. [Brown's penalty] was kind of a little debatable call, I thought, but that's the way the game goes sometimes."