Duliba made his major league debut on August 11, 1959, against the San Francisco Giants at Busch Stadium. He pitched two scoreless innings in the 5–4 Cardinal loss. He struck out one batter, outfielder Jackie Brandt. He earned his first big league save eighteen days later in a home game against the Cincinnati Reds.\n', '

After relieving in 28 games with a 2.06 earned run average for the Cardinals in 1962, he was traded to the Los Angeles Angels for relief pitcher Bob Botz. In 1964, Duliba had his busiest season, finishing in the American League top ten in games pitched (58) and games finished (35). He was 6–4 with nine saves and an ERA of 3.59 for the Angels that season.\n', '

Traded to the Boston organization the following spring, Duliba appeared in 39 games for the 1965 Red Sox and led the team\'s pitching staff in earned run average (3.17). Duliba closed out his major league career with the A\'s in 1967, their last season in Kansas City.\n', '

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