Connor McDavid, who led the NHL with 105 points (33 goals, 72 assists), and Leon Draisaitl, who was second with 84 points (31 goals, 53 assists) each was held without a point for Edmonton.
"I think we had some nerves and some jitters in the first period," McDavid said. "We kind of got through that even, but then I thought we took over in the second and did a lot of good things. We put a lot of pucks on net and hemmed them in there for chunks at a time. You'd like to come out of that period with a lead, but ultimately that wasn't the case. The third period was back and forth, and a tight hockey game, and they get a bounce and that's the way it goes."
Game 2 is here Friday (9 p.m. ET; CBC, SN, TVAS, NBCSN).
Teams that win Game 1 are 490-222 (68.8 percent) winning a best-of-7 NHL playoff series, including 7-1 in the first round last season.
"I thought that both teams were actually tentative in some of their play with the puck early, which is understandable," Jets coach Paul Maurice said. "It was a little more physical at times so there weren't a lot of plays made. And then neither team generated much off the rush, which is prototypical of playoff hockey. I thought they did a better job getting to our crease and scrumming pucks. Where Connor [Hellebuyck] was really good was within two feet of the blue paint. I think that's an area we have to improve on."
Puljujarvi scored at 8:24 of the second period to give the Oilers a 1-0 lead. He was first to a loose puck in front following shot from Tyson Barrie from the point, which was blocked by Jets defenseman Dylan DeMelo.
"I think I just tried to work hard and make good plays and play smart," Puljujarvi said. "It was a hard game and hopefully we can win the next one."