He played in Major League Baseball as a right-handed pitcher between 1964 and 1982 for the Philadelphia Phillies, St. Louis Cardinals, Boston Red Sox, Cleveland Indians and the San Diego Padres.

Wise was the last player from the 1964 Philadelphia Phillies team to be active in the major leagues, pitching two innings of relief (7th and 8th) for the Padres against the Los Angeles Dodgers on April 10, 1982.

[5] He spent all of 1965 and the early part of 1966 with the Phillies' top minor league affiliate (the Arkansas Travelers in 1965 and the San Diego Padres in 1966) before making the majors for good.

The highlight of Wise's Philadelphia career took place that year on June 23 when he overcame the flu to no-hit the Cincinnati Reds in a 4–0 win at Riverfront Stadium.

He also contributed a pair of homers, a one-out two-run home run off Ross Grimsley in the fifth and a leadoff solo shot off Clay Carroll in the eighth.

[7] Wise, Wes Ferrell (1931), Jim Tobin (1944), and Earl Wilson (1962) are the only pitchers to throw a no-hitter and hit a home run in the same game.

On September 18 against the Chicago Cubs, he completed a string of retiring 32 batters in a row, four shy of Harvey Haddix's Major League record, also driving in the winning run in the 12th inning.

The owner of the St. Louis Cardinals, Gussie Busch, ordered his team to trade its star left-handed pitcher, Steve Carlton, after a contract squabble.

Since all of baseball knew of the trade mandate, teams drove very hard bargains, and the Phillies' offer of Wise was the best St. Louis could do.

Wise would have joined Cy Young and Jim Bunning as pitchers who had hurled no-hitters in both leagues (Nolan Ryan, Hideo Nomo and Randy Johnson have done it since).

On March 30, during spring training, he was traded by the Boston Red Sox with Ted Cox, Bo Díaz and Mike Paxton to the Cleveland Indians for Fred Kendall and future Hall of Fame starter and reliever Dennis Eckersley.