The highest-scoring team in National Hockey League history was shut out tonight in the opening game of the Stanley Cup final.

Veteran goaltender Billy Smith stopped all 35 shots taken by Edmonton as the New York Islanders continued relentlessly toward a fourth straight Cup with a 2-0 victory over the Oilers.

Only one goal against Edmonton's Andy Moog meant anything. It was produced by Alberta native Duane Sutter at 5:36 of the first period, as New York benefited from two consecutive deflections.

Stefan Persson's shot from the left point was partially blocked and the puck skidded onto the stick of Bob Bourne in the left-wing circle. An Edmonton defender got a piece of Bourne's shot, too, and this time the puck went to Sutter just outside the right post.

Moog, committed to the right side, was unable to shift quickly enough to foil Sutter. But with more than 54 minutes remaining and with Edmonton having produced 74 goals in 12 previous playoff games, the crowd of 17,498 was not overly concerned.

As it turned out, however, that was it until Ken Morrow fired the puck into an empty net with 12 seconds to play. For the Oilers, it was the first shutout defeat in 198 games, since Smith carried the Islanders to a 5-0 victory here March 12, 1981.

For Smith, this was the fifth playoff shutout and raised his Stanley Cup record to 72-22. In his last three appearances in the Stanley Cup final, he has permitted only one goal.

"Any time you shut out a great offensive team like the Edmonton Oilers, you feel great," said a smiling Smith.

"This was maybe the best loss we've ever had," said Edmonton superstar Wayne Gretzky, who did not feel great. "We ran into a fabulous goaltender and just couldn't put the puck in the net. But I thought we played a great game."

On five occasions in the third period alone, it appeared that the Oilers were certain to score the tying goal, as they forced the tiring Islanders back and sent the puck through and around the crease.

Early in the period, with each team two men short, Paul Coffey's pass left Gretzky alone in front, but he fell over Smith before he could release the shot.

"I thought Gretzky had me, but I kicked the feet out from under him as he cut across," Smith said. "I guess I got him just in time."

Midway through the period, Gretzky skated in from the right wing, stopped and drew the defense to him, then passed to Glenn Anderson for an open shot on the left side. Anderson was inches wide of the far post.

With six minutes left, Kevin Lowe skated down the slot and lined one off the post at Smith's left.

With 3 1/2 minutes remaining, Gretzky picked off Denis Potvin's pass, eluded the other defender, Persson, and aimed for the lower right corner. Smith kicked it out.

Edmonton continued to force the play and, with 30 seconds on the clock, Dave Lumley passed to Ken Linseman, who attempted to relay it to a wide-open Gretzky sitting at Smith's doorstep. Potvin lunged and knocked it past the post, setting the stage for Morrow's clincher.

"I was just ready to put it in the net," Gretzky said. "I had it teed up, as they say. But Potvin made a great play to tip it wide. Any other night he might have tipped it into the net, but this just wasn't meant to be for the Edmonton Oilers tonight."

"We didn't seem to get any bounces tonight," echoed Coach Glen Sather. "Lowe hit the post head on, Gretzky was open and Potvin just got the blade of his stick on it. It seemed like it wasn't our night."

Besides his wide shot in the third period, Anderson twice was turned back by Smith after skating around defenseman Tomas Jonsson and carrying the puck into the crease.

Moog had his moments in the Edmonton net, although the Islanders had only 24 shots. As the Oilers turned on full throttle in the bid to tie it, both John Tonelli and Bob Nystrom came in alone, to be frustrated in turn.

New York was forced to play without high scorer Mike Bossy, who had a severe case of tonsillitis. Bossy came to the rink with the team, but was ordered back to his hotel.

"When we found out Boss wasn't playing, we went from plan A to plan B very quickly," said Coach Al Arbour. "We've had a lot of frustrating times this year, but the guys have dug deep and come through.

"We were backing up as they were pressing in the third period, but we scratched and clawed and banged them enough to throw them off a little bit. And when we let down in front of him, Smitty was there to keep it out. He's done it time and again in the Stanley Cup playoffs."