Born in Winston-Salem, North Carolina, Cardwell signed with the Philadelphia Phillies as an amateur free agent in 1954.

Two days later, he no-hit the St. Louis Cardinals 4–0 in the second game of a doubleheader at Wrigley Field—the first no-hitter ever thrown by a pitcher in his first start with a new team.

A month later, the Cardinals traded him to the Pittsburgh Pirates in a deal that sent former National League MVP Dick Groat to the Redbirds.

In December 1966, he was traded with Pirates outfielder Don Bosch to the New York Mets for pitcher Dennis Ribant and utilityman Gary Kolb.

In the 1969 season, he went 8–10 in a rotation with pitchers Tom Seaver, Jerry Koosman, Nolan Ryan and Gary Gentry, helping them win the World Series.

This victory, the ninth of a ten-game winning streak for the Mets, came two days after the Mets had taken over first place for good in the National League East (in 1969 the two leagues had been split into two divisions) by leapfrogging past the Chicago Cubs, who had been in first place for much of the season before stumbling down the stretch.