Dave McKay hit a solo homer in the seventh inning to give the Oakland A's a 4-3 victory yesterday over host Kansas City, pushing the Royals' season into overtime in search of the second-half championship of the American League West.

Although the 1981 season is over for everyone else, the Royals must travel to Cleveland today to make up a doubleheader with the Indians. Kansas City has a half-game lead over Oakland and needs one victory in Cleveland to clinch the second-half title and secure two home games against the A's in the divisional playoff.

That playoff begins in Kansas City on Tuesday.

McKay's fourth homer of the season came off Larry Gura (11-8) with one out in the seventh to snap a 3-3 tie after the Royals had scored twice in the sixth on singles by Frank White, Willie Aikens, Amos Otis and Hal McRae to deadlock the game.

Dwayne Murphy drew a one-out walk off Gura in the first and came all the way around to score on Tony Armas' double. Mickey Klutts then singled Armas home to stake starter Matt Keough to a 2-0 lead before he ever took the mound.

The Royals got one run back in the second whe Otis singled, stole second, went to third on a balk and scored on Clint Hurdle's single. But the A's restored the two-run cushion in the third on singles by Rickey Henderson and Murphy and a sacrifice fly by Cliff Johnson.

Keough ran his record to 10-6 by scattering seven hits over 7 1/3 innings. He got relief help from Tom Underwood and Dave Beard, who got his third save in pitching the final 1 1/3 innings.

Meanwhile, Milwaukee lost to Detroit. Kirk Gibson's third single knocked in the winning run in the ninth inning and Milt Wilcox scattered eight hits in leading the visiting Tigers to a 3-2 victory. The Brewers will open their AL East playoff series Wednesday at home against the Yankees.

In Cleveland, Dwight Evans homered twice and doubled, scoring three times as the Boston Red Sox closed with a 6-2 victory over the Indians.

In Seattle, homers by Terry Bulling and Tom Paciorek gave the Mariners a 2-0 victory over the Toronto Blue Jays.

In Chicago, Jerry Hairston, who hit a grand slam in the eighth, capped a four-run ninth inning with an RBI single to lift the White Sox to a wild 13-12 victory over the Minnesota Twins.

In Arlington, Tex., Don Baylor cracked four hits, drove in two runs and scored another to lead California past Texas, 9-2.

In the National League, Gary Woods singled home the tie-breaking run in the top of the ninth inning as the visiting Houston Astros defeated the Los Angeles Dodgers, 5-3. The same two teams will begin their West playoff series Tuesday in Houston.

In Philadelphia, Lonnie Smith extended his hitting streak through 23 games with a third-inning double and scored the winning run on a wild pitch as the playoff-bound Phillies beat the Chicago Cubs, 2-1.

In New York, Pete Falcone pitched a seven-hitter and Rusty Staub doubled in the winning run as the Mets edged the Expos, 2-1. The Expos open their NL East playoff series at home Wednesday against Philadelphia.

In San Francisco, pinch hitter Milt May's infield out in the eighth inning scored Gene Ransom with the winning run as the Giants nipped San Diego, 4-3.

In Pittsburgh, Bob Shirley and two relief pitchers combined on a four-hitter to pace the St. Louis Cardinals to a 4-0 victory over the Pirates

In Cincinnati, Mario Soto hurled a one-hitter -- Chris Chambliss' leadoff single in the second inning -- to pitch the Reds to a 3-0 decision over the Atlanta Braves.