Ovechkin scored into an empty net with 56 seconds remaining to tie Yzerman and complete the Capitals' five-goal comeback after they trailed 4-1 entering the third period. It was his third goal of the game.
Ovechkin scored on a breakaway at 10:22 of the first period to tie Lemieux with his 690th goal, then passed Lemieux on a left-wing rush to pull Washington within 4-3 at 5:18 of the third.
With his 26th NHL hat trick, and second in as many games, the 34-year-old tied Maurice Richard for eighth in League history.
"It's amazing. It's something special," Capitals forward Jakub Vrana said. "It's obviously really nice to see him getting these records. ... He's got a special shot. The best shot I've ever seen. I'm really happy for him."
Ovechkin has 692 goals in 1,133 games and 15 seasons with the Capitals. Yzerman scored that many in 1,514 games and 22 seasons with the Detroit Red Wings before retiring in 2006.
"Those are players that I can just speak personally on this one, that I used to look up to and always considered it an honor to play against them," said Capitals coach Todd Reirden, who was an NHL defenseman from 1999-2004. "… To now see Ovi passing them and still have plenty of games in front of him to continue to move forward from there is pretty awesome to see."
Ovechkin is tied with Toronto Maple Leafs center Auston Matthews for second in the NHL this season with 34 goals, two behind Boston Bruins forward David Pastrnak for the League lead. Ovechkin is the second player to score at least 30 goals in each of his first 15 NHL seasons, joining Gartner (1979-80 through 1993-94).
"To me, at this point, he would be the greatest goal-scorer of all time," said Islanders coach Barry Trotz, who coached Ovechkin with the Capitals from 2014-18. "We see how he shoots the puck and the angles he is able to place in the spots where he gets the pass … and he finds a way to get it into the net or through a spot. For the most part, you don't see the shot, you hope it just hits you as a goaltender."
Ovechkin has eight goals in his past three games, including a hat trick in a 5-2 win against the New Jersey Devils on Thursday. This is the third time -- all in the past three seasons -- he has had a hat trick in consecutive team games. Ovechkin is the third player in NHL history to do that; Joe Malone did it four times, Gretzky three.
"It's unbelievable. I think his stats show how good he is," said Capitals defenseman Dmitry Orlov, who has been Ovechkin's teammate for eight seasons. "He already gets a milestone in almost every [game]. It's pretty cool to see, and he's a good teammate. He's our leader, and I think he showed that today."
Ovechkin scored twice in a 2-0 win against the Carolina Hurricanes on Monday, when he passed Teemu Selanne (684 goals) for 11th. It is the first time in his NHL career he has had three straight multigoal games.
"He's been in a really good place the last three games," Reirden said. "Obviously eight goals in the past three games is phenomenal. He was going, and we needed to get him out there."
NHL.com staff writers Tom Gulitti and David Satriano contributed to this report