NEW YORK, NOV. 10 -- Philadelphia Phillies reliever Steve Bedrosian, who led the major leagues with 40 saves and figured in over half of his team's victories, won the National League Cy Young Award today by the slimmest margin in the award's 20-year history.

Bedrosian, who set a major league record with saves in 13 consecutive appearances, edged Chicago's Rick Sutcliffe, 57 points to 55, in balloting by the Baseball Writers Association of America. Rick Reuschel, who played for Pittsburgh and San Francisco, finished one point behind Sutcliffe.

Voting was based on five points for first place, three for second and one for third. Two writers from each NL city took part in the balloting.

The closest vote prior to this year's was the one in 1981, when Los Angeles' Fernando Valenzuela outpolled Cincinnati's Tom Seaver by three points.

Bedrosian had a 5-3 record and an earned run average of 2.83 in 1987. He struck out 74 and walked 28 in 89 innings. Also, he converted 40 of 48 save opportunities. Despite his outstanding season, the Phillies finished tied for fourth in the NL East with an 80-82 record.

"This is the ultimate," Bedrosian said during a news conference in Philadelphia. "I'm a team player, but this is an individual thing. The thing I'd like the most is to be in the World Series. But this is the ultimate for a pitcher. I'll never forget it as long as I live."

Sutcliffe, the 1984 Cy Young winner, had an 18-10 record and a 3.68 ERA in 1987. Reuschel was 13-9 with a 3.09 ERA.

Bedrosian is the third reliever to win the NL Cy Young Award since the leagues started having separate honors in 1967. Chicago's Bruce Sutter won in 1979 and Los Angeles' Mike Marshall won in 1974.

It is fourth time this decade that a member of the Phillies has won the NL Cy Young Award. Steve Carlton won in 1980 and 1982, and John Denny won in 1983.

For winning the award, Bedrosian received a $100,000 bonus from the Phillies.

The 29-year-old right-hander was traded from Atlanta to Philadelphia on Dec. 10, 1985, for catcher Ozzie Virgil and pitcher Peter Smith. In his first season with the Phillies, Bedrosian had 29 saves, an 8-6 record and a 3.39 ERA.

Bedrosian spent five seasons in Atlanta, where he compiled a 34-39 record. In his final season with the Braves, he switched from relieving to starting and had a 7-15 record and a 3.83 ERA.Complete balloting results, Page B11