Jagr had an assist on Florida’s first goal to tie Gordie Howe for third all-time in points with 1,850. Jagr, in his 22nd season, ranks third in goals with 743 and his 1,107 assists are sixth.
He is 37 points behind Mark Messier for second.
"Jags finds a way to get his points and he played a pretty solid game," Florida coach Gerard Gallant said.
Matt Duchene and Mikkel Boedker also scored and Tyson Barrie had two assists for Colorado.
The Avalanche have 70 points and kept pace with Minnesota for the second wild card in the Western Conference. The Wild beat Toronto for their third straight win and are ahead of Colorado by virtue of having played one fewer game.
The Avalanche are tied with Minnesota thanks to their new No. 1 goaltender. Pickard was named the starter after Semyon Varlamov struggled of late. He gave up three goals in the third period against Detroit on Saturday and three more in the first period at Minnesota on Monday.
Colorado coach Patrick Roy went with Pickard against the Panthers and he rewarded him with a big night.
"The thing that I like about him is his swagger," Roy said. "He seems very confident right now in front of the net. He looks big and he's moving well. I love that intensity that he's bringing, the compete level that he's bringing on the ice."
Colorado had to hold on in the third to get the key two points. Florida came strong offensively from the start of the period and never let up, but Pickard stopped every chance.
"It seemed like a tale of two games," Pickard said. "In the first two periods they were really looking for that late guy, they were really selective on their shots. Then they came out in the third and literally threw everything at the net."
The Avalanche had chances to extend the lead. Nathan MacKinnon was awarded a penalty shot when he was hooked on a breakaway late in the third period but Luongo made a glove save.
"I was watching some video on his shootout moves and usually when he came in with speed, he would go backhand blocker side but for some reason he went back to his forehand and shot it, and my glove just happened to be there," Luongo said. "It was kind of a lucky save."
A minute later he made sprawling save on Jarome Iginla to keep it a one-goal game.
Jagr got the historic point with the second assist on Gudbranson's goal at 9:42 of the first that tied the game at 1. Landeskog had given Colorado the early lead with a power-play goal at 5:45.
He nearly set up a tying goal early in the third period that would have moved him past Howe. He finished with four shots, three of which came in the third period
"It doesn't matter," he said. "We put ourselves in a hole, just pushing in the door, but the door closed."
Boedker, acquired from Arizona on Monday, got his first goal with Colorado to give the Avalanche a 2-1 lead late in the first.
Duchene made it 3-1 with his 27th at 4:55 of the second and Campbell got one back for Florida with his sixth at 12:42 of the second.
NOTES: Avalanche D Eric Gelinas was out with a back injury. Gelinas was acquired from New Jersey on Monday and played Tuesday in Minnesota. ... Panthers forwards Teddy Purcell and Jiri Hudler were not with the team while they straighten out their paperwork for their U.S. visas. Florida traded for them Saturday and they played in Winnipeg on Tuesday.