Born in Orient, Iowa, Vance played in minor league baseball for a decade before establishing himself as a major league player. His contract was purchased by the Brooklyn Robins from the New Orleans Pelicans in 1922. The Robins wanted to acquire catcher Hank DeBerry, but the Pelicans refused to complete the deal unless Vance was included in the transaction. DeBerry would become Vance's personal catcher during his tenure with Brooklyn. In 1922, he produced an 18–12 won-loss record with a 3.70 earned run average and a league-leading 134 strikeouts. His best individual season came in 1924, when he led the National League in wins (28), strikeouts (262) and ERA (2.16) (see Triple crown) en route to winning the National League Most Valuable Player Award. He set the then-National League record for strikeouts in a nine-inning game when he fanned 15 Chicago Cubs in a game on August 23, 1924. (He struck-out 17 batters in a 10-inning game in 1925.)
On September 24, 1924, Vance struck out three batters on nine pitches in the second inning of a 6–5 win over the Chicago Cubs. Vance became the fifth National League pitcher and the seventh pitcher in Major League history to accomplish the nine-strike/three-strikeout half-inning. He finished the season with 262 strikeouts, more than any two National League pitchers combined (Burleigh Grimes with 135 and Dolf Luque with 86 were second and third respectively). That season, Vance had one out of every 13 strikeouts in the entire National League.
Vance's play began to decline in the early 1930s, and after bouncing to the St. Louis Cardinals (becoming a member of the team known as the Gashouse Gang), Cincinnati Reds and back to the Dodgers, he retired after the 1935 season. Vance led the league in ERA three times, wins twice, and established a National League record by leading the league in strikeouts in seven consecutive years (1922–1928). He retired with a 197–140 record, 2045 strikeouts and a 3.24 ERA – remarkable numbers considering he only saw 33 innings of big league play during his twenties.
Vance was also involved in one of the most famous flubs in baseball history, the "three men on third" incident during the 1926 season. With Vance on second and Chick Fewster on first, Babe Herman hit a long ball and began racing around the bases. As Herman rounded second, the third base coach yelled at him to go back, since Fewster had not yet passed third. Vance, having rounded third, misunderstood and reversed course, returning to third. Fewster arrived at third. Herman ignored the instruction and also arrived at third. The third baseman tagged out Herman and Fewster; Vance was declared safe by rule.