Ovechkin, 36, scored his 35th goal of the season at 13:23 of the second period, creating the scoring chance with a punishing check on Calgary defenseman Chris Tanev in the corner. He tied Jagr by scoring his 36th goal into an empty Calgary net with 1:48 remaining in the third period.
"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.''
Ovechkin has 766 goals in 1,253 games in the NHL dating back to 2005-06. It took Jagr 1,733 games to reach 766 goals. He missed three seasons (2008-09 through 2010-11) while playing in the Kontinental Hockey League.
Jagr, 50, last played in the NHL during the 2017-18 season. He's continued his career with Kladno of the Czech Extraliga, competing in their season finale on Tuesday at Prague's O2 Arena, in a game that raised funds for Ukrainian families seeking asylum in the Czech Republic after Russia's invasion.
It was Ovechkin's 120th career game-winning goal, putting him one goal behind Gordie Howe for second all time, trailing only Jagr (135). Ovechkin recorded his 157th career multigoal game, leaving him one shy of tying Brett Hull (158) for the second-most multigoal games in NHL history. Goal No. 766 was Ovechkin's 47th career empty net goal, trailing only Wayne Gretzky (56).
Of course, there's a greater chase at hand for Ovechkin and Gretzky. Ovechkin now trails Gretzky's all-time NHL goals record (894) by 128 goals. If Ovechkin passes Jagr, the next benchmark will be Gordie Howe's 801 career goals.
Ovechkin has scored in three straight games.
"I think guys are just excited for him,'' said Washington coach Peter Laviolette. "We don't talk about it much. I think everybody knows what's going on and it's awesome to be a part of.''
After Elias Lindholm's second goal with 40 seconds left got Calgary within one, Ovechkin had a chance for a hat trick in the waning seconds, but his shot at the empty net was deflected by Lindholm.
"I was hoping so, but it hit his skates. It's OK. I'll take it tomorrow,'' Ovechkin said.
Nic Dowd, who scored the go-ahead goal for the Capitals as Washington rallied in the third period, thought he and his teammates were about to witness history.
"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.''
It was Ovechkin's first road game following his comments on Feb. 25 about Russia's invasion of Ukraine. Ovechkin has been an ardent supporter of Russian President Vladimir Putin over the years. In 2017, he campaigned on behalf of Putin by starting a social media movement called Putin Team.
"Please, no more war. It doesn't matter who is in the war -- Russia, Ukraine, different countries -- we have to live in peace," Ovechkin said.
Flames fans frequently booed Ovechkin whenever he touched the puck on Tuesday night, especially early in the game. After the game, Ovechkin spoke only about the contest.
The Associated Press contributed to this report.