He was traded with Jim Beauchamp, Chuck Taylor and Chip Coulter from the Cardinals to the New York Mets for Art Shamsky, Jim Bibby, Rich Folkers and Charlie Hudson on October 18, 1971. His most productive season came in 1973, when he went 8–4 with a 3.35 ERA and 63 strikeouts in 96 innings of work to become an integral contributor for the Mets' National League pennant run. He appeared once in the National League Championship Series (NLCS) and three times in the World Series and was the losing pitcher once in each of the two postseason rounds. He surrendered a twelfth-inning one-out solo home run to Pete Rose that won Game 4 of the NLCS for the Cincinnati Reds. In the eleventh inning of Game 3 of the Fall Classic, Parker allowed a one-out walk to Ted Kubiak who advanced to second base on a Jerry Grote passed ball when Ángel Mangual struck out and scored the Oakland Athletics' winning run on Bert Campaneris' single to center field.