The National League's win in the 35th All-Star Game tied the series at 17-17 -- marking the first time since the series started in 1933 that the leagues were even in wins.
The American League held a 4-3 lead going into the bottom of the ninth on July 7 in the first All-Star Game played at Shea Stadium, home of the New York Mets.
The bottom of the ninth opened with Giants center fielder Willie Mays drawing a walk from Boston Red Sox reliever Radatz, who had already worked two scoreless innings.
Mays stole second and scored the tying run after a pop-fly single to short right by San Francisco teammate Orlando Cepeda -- Mays advancing to third and scoring on a wild throw to the plate by Yankees first baseman Joe Pepitone with Cepeda moving to second.
Radatz retired Cardinals third baseman Ken Boyer for the first out to keep pinch-runner Curt Flood of the Cardinals at second with the winning run. After intentionally walking Cincinnati catcher Johnny Edwards, Radatz struck out pinch-hitter Hank Aaron of the Milwaukee Braves to move to within an out of sending the game into the 10th inning.
The next hitter was Philadelphia's Callison, who had entered the game as a pinch-hitter for Phillies pitcher Jim Bunning in the bottom of the fifth and had remained in right field for starter Roberto Clemente.
Callison drove a Radatz fastball into the right-field stands to give the National League its sixth win in the last seven games. Callison was named the All-Star Game's Most Valuable Player.
Callison's homer marked the fourth time the lead changed hands.
The American League took a 1-0 lead in the top of the first off National League starter Don Drysdale of the Dodgers when Angels shortstop Jim Fregosi singled, moved to second on a passed ball by catcher Joe Torre of the Braves and scored an unearned run on a two-out single by Minnesota Twins left fielder Harmon Killebrew.
The National League took a 2-1 lead in the bottom of the fourth when Chicago Cubs left fielder Billy Williams and Boyer hit solo homers off Kansas City Athletics pitcher John Wyatt.
The National League extended its lead to 3-1 an inning later when Clemente singled with two out against the Twins' Camilo Pascual and scored on a double by Pirates teammate Dick Groat's double.
The American League tied the game with two runs in the top of the sixth against Chris Short of the Phillies. Yankees center fielder Mickey Mantle and Killebrew hit back-to-back singles with one out and scored on a two-run triple by Baltimore Orioles third baseman Brooks Robinson.
The American League took the lead at 4-3 in the seventh against Turk Farrell of Houston, who hit Yankees catcher Elston Howard with a pitch to start the inning. Howard moved to third on a double by Kansas City pinch-hitter Rocky Colavito and scored on a sacrifice fly by Fregosi.
Killebrew was 3-for-4 and Robinson was 2-for-4 with two RBIs for the American League. Boyer was 2-for-4 for the National League.
Both starting pitchers were from Los Angeles. Dean Chance of the Angels allowed two hits over three scoreless innings for the American League. Drysdale allowed one unearned run on two hits over three innings for the National League.
Bunning followed Drysdale and struck out four while allowing two hits in two scoreless innings. Juan Marichal of the Giants pitched a perfect ninth for the win.