On April 17, 1964, Harkness led off for the Mets in the bottom of the first inning and had a single off of Bob Friend in the third inning to become the first Mets player to bat and the first to get a hit in the team's first game played at Shea Stadium as part of a 4–3 loss to the Pittsburgh Pirates.
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Harkness made his major league debut on September 12, 1961 against the Phillies, working out a walk in five pitches against pitcher Chris Short as a pinch hitter in the ninth inning in a 19–10 loss at the Los Angeles Memorial Coliseum.
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