Puljujarvi, the fourth pick of the 2016 NHL Draft, spent 28 games with the Oilers last season (one goal, seven assists) when he was the youngest player to start the season on an NHL roster in 2016-17.
He was sent to Bakersfield of the American Hockey League on Jan. 9 and had 28 points (12 goals, 16 assists) in 38 games.
At training camp this season, he was on the bubble and was sent to the AHL as one of the final cuts.
After four points (one goal, three assists) in 10 games in Bakersfield, he was recalled by the Oilers on Nov. 10 and with 14 points (nine goals, five assists) in 30 games, has been earning more trust from his coaches and teammates, and more confidence in himself.
"The sky is as tall as he wants it to be," Oilers captain Connor McDavid said. "He's big, skates well, is confident, has a great shot. But I think it all goes back to his size. He's 6-4, still young, trying to (grow) into his body. He'll be that solid-on-his feet, good puck-battle guy. Good in front of the net. The sky's the limit for him."
Draisaitl, who was the center for Puljujarvi and Jujhar Khaira on Saturday, continued the endorsement.
"Everyone is really excited for him," Draisaitl said. "Him coming over from Finland, I can't imagine how hard it is, not being able to speak the language.
"I think he's coming along. You could see it today. He's a very dynamic player and a lot of fun to play with."
Draisaitl said he could see a little of himself in Puljujarvi. After Draisaitl was selected No. 3 in the 2014 NHL Draft, he stayed with the Oilers for 37 games (two goals, seven assists) before he was sent back to junior with Kelowna of the Western Hockey League.