After making his debut in 1923 and spending three seasons with the Braves, Padgett's contract was purchased by the Cleveland Indians, where he spent the next two years of his career before playing his last game on July 30, 1927.

Padgett is best known for turning the fourth unassisted triple play in Major League Baseball history on October 6, 1923.

"[3][4] Padgett began his career for the Memphis Chicks, a minor league baseball team that were members of the Southern Association.

[1][5] He made his major league debut for the Braves on October 3, 1923, at the age of 24,[1] entering the game as a pinch-hitter for pitcher Joe Oeschger.

[12][13] After being drilled in the head by a pitch, Padgett was permitted by the umpires to have a pinch runner replace him while he sat out and recuperated from his dizziness.

[5] Padgett arrived in Cleveland and served as the temporary replacement for the injured Johnny Hodapp, who suffered from sprained ankle at the time.

[18] Padgett was granted an unconditional release in 1930,[19] whereupon he joined the Charlotte Hornets, who were ranked as Class B in the South Atlantic League.

[17] In the middle of that season, he signed with the Reading Keystones of the International League[19] and played for them for the remainder of the year before retiring completely from baseball.