Wynn was nicknamed "The Toy Cannon" because his bat was described as having a lot of "pop" for his small size at 5 ft 9 in (1.75 m) and 160 lb (73 kg).

After the 1962 season, the Houston Colt .45s selected Wynn in the 1962 first-year minor league player draft.

Wynn began the 1963 season with the Double-A San Antonio Bullets in the Texas League, and while there split his time between shortstop and third base while batting .288 with 16 home runs in 78 games.

He opened the season as the Colt .45s starting center fielder, but was sent back to the minor leagues in June, with Mike White taking over.

His 1966 season ended abruptly after 105 games after breaking his left arm crashing into the outfield wall at Connie Mack Stadium chasing down a Dick Allen fly ball resulting in a game-winning, inside-the-park home run for Allen and the Philadelphia Phillies in the bottom of the 10th inning on August 1, 1966.

The shot, which came in the eighth inning of the Astros' 8–3 loss to the Cincinnati Reds, cleared the 58-foot scoreboard in left-center field and landed on Interstate 75 outside the stadium.

Five days later, Wynn became the first Houston batter to hit three home runs in one game as his Astros defeated the San Francisco Giants 6–2 at the Astrodome.

He successfully got on base at least once in 52 straight games from June 4 to August 3; the mark was tied by Greg Gross six years later, which still stands as a franchise record.

Wynn was traded from the Astros to the Los Angeles Dodgers for Claude Osteen and minor-league right-handed pitcher David Culpepper at the Winter Meetings on December 6, 1973.

Wynn homered in the 2nd inning of the All-Star Game that year, leading the National League to a 6-3 victory.

On November 17, 1975, he (along with Lee Lacy, Tom Paciorek and Jerry Royster) was traded to the Atlanta Braves for Dusty Baker and Ed Goodson.

In the five decades since his last game with Houston, only Jeff Bagwell, Lance Berkman, and Craig Biggio have passed him.

On the October 7, 1974 episode of The Tonight Show Starring Johnny Carson, Wynn faced women's softball pitcher Rosie Black.