 Kọ itẹsiwaju fun paragirafi yii - O ti ṣe paṣipaarọ pẹlu Jim Beauchamp, Chuck Taylor ati Chip Coulter lati awọn kaadi si awọn New York Mets fun Art Shamsky, Jim Bibby, Rich Folkers ati Charlie Hudson ni Oṣu Kẹwa Ọjọ 18, Ọdun 1971. Akoko ti o ni ipa julọ wa ni ọdun 1973, nigbati o lọ 84 pẹlu 3.35 ERA ati awọn ikọlu 63 ni awọn innings 96 ti iṣẹ lati di alabapin pataki fun Mets National League pent run. Ó fara hàn lẹẹkan nínú National League Championship Series NLCS : ó sì jẹ ọkan lára àwọn tó pàdánù nínú ìpele méjèèjì tí wọn fi ń ṣe eré ìdárayá. O fi home run kan silẹ fun Pete Rose ti o ṣẹgun Ere 4 ti NLCS fun Cincinnati Reds. Ni inning kẹrindinlogun ti Ere 3 ti Fall Classic, Parker gba laaye lati rin si Ted Kubiak ti o lọ si ipilẹ keji lori bọọlu Jerry Grote ti o kọja nigbati Ángel Mangual kọlu ati gba igbasilẹ ti o ṣẹgun ti Oakland Athletics lori Bert Campaneris kan si aaye aarin. 