PERTH, Australia, Jan. 4--Alex Olmedo, the Peruvian who starred for the U.S. in its Davis Cup victory over Australia, won his opening match today in the Western Australian Tennis Championships.

Olmedo defeated Frank Taaffe of Australia 6-1, 6-1, 6-3 in play at the Royal King's Park Courts.

There were no surprises in other matches with other U.S. cup team members winning handily over Australian opponents.

Celtics Beat Royals

CINCINNATI, Jan. 4--Boston's highflown Celtics had to beat off successive threats Sunday to clinch an 111-108 victory over Cincinnati's Royals in the dying seconds of an afternoon National Basketball Association game.

Two good free throws in the last 38 seconds by veteran Bob Cousy plus some of his noted blurry ball-handling set the issue.

The final quarter continued a duel between Cousy and big Wayne Embry, who kept the Royals pressing with his 12 point contribution.

A crowd of 2,533 saw the Celtics consolidate their hold on the division lead and set their season mark at 24-10. Cincinnati has beaten Boston once in five games this year.

Lakers Defeat Warriors

PHILADELPHIA, Jan. 4--The Minneapolis Lakers took advantage of injuries and two shooting lapses to run away today with an 111-95 victory over the Philadelphia Warriors in a nationally-televised National Basketball Association game.

High men for Minneapolis were Elgin Baylor with 28 points and Dick Garmaker who scored 24 before fouling out in the fourth period. It was the Lakers' fifth straight triumph.

Syracuse Nationals Win

SYRACUSE, N.Y., Jan. 4--The Syracuse Nationals outsprinted the Detroit Pistons for a 118-94 victory in their National Basketball Association game today. Despite suffering a back injury, John Kerr had one of his finest games as a pro, leading the winners with 31 points.

Bruins Lose

CHICAGO, Jan. 4--The Chicago Black Hawks took sole possession of second place in the National Hockey League tonight when they pounded the Boston Bruins 5-3 in Chicago Stadium.

Ted Lindsay's two goals--his eighth and ninth of the year--helped the Hawks extend their unbeaten string to six.