Ovechkin scored No. 765 at 13:23 of the second period with a wrist shot from the left face-off circle to tie it 2-2, and No. 766 into an empty net with 1:48 remaining in the third period to give the Capitals a 5-3 lead.
"Obviously, it's always nice to hear those kind of milestones, numbers," Ovechkin said. "It's pretty big, obviously, and how I always said, being with those names and in this company, it's a pretty cool moment."
The 36-year-old trails Gordie Howe (801) and Wayne Gretzky (894) for the most in NHL history.
Jagr also scored No. 766 at Calgary while playing for the Flames against the Detroit Red Wings on Nov. 9, 2017.
"He's a natural goal-scorer," Jagr said of Ovechkin last month. "The game has changed a lot, and it's for his good because he can keep up with the speed. He can keep up with the speed easily. He's got a great shot. But a huge advantage for him is nobody, I mean nobody, is as strong as him. So he cannot be stopped if he doesn't want to."
Ovechkin nearly passed Jagr with two seconds left, but his shot toward the empty net was blocked by Calgary center Elias Lindholm.
"Yeah. I was hoping so, but it hit his skates," Ovechkin said. "It's OK. I'll take it tomorrow."
Capitals forward Nic Dowd thought Ovechkin would score a third goal.
"I couldn't believe that one got blocked at the end, but it was awesome," Dowd said. "Obviously, we're super excited for him, and guys are trying to find him all over the ice and just to be a part of it and simply watch it, he's the best. So really happy for him."
Teammate Evgeny Kuznetsov said he wasn't aware of the significance of Ovechkin's second goal.
"I didn't know actually when he scored that he was tying. I think the next one will be big for him," Kuznetsov said. "I think that's one of the first milestones he probably hit in the seven, eight games of playing with him that probably is pretty big for him."