On January 16, 1979, Clements succeeded Democrat Dolph Briscoe as governor of Texas. To win the position, he first defeated State Representative Ray Hutchison in the Republican primary by a lopsided vote of 115,345 to 38,268. Hutchison, a prominent Dallas attorney, is the second husband of Texas State Treasurer (1991–1993) and U.S. Senator Kay Bailey Hutchison, who served from 1993 to 2013. Clements won the November 1978 general election by narrowly defeating Democratic former Texas Supreme Court Chief Justice John Luke Hill, who served six years as state attorney general. Clements polled 1,183,828 votes (49.96 percent) to Hill's 1,166,919 ballots (49.24 percent). The La Raza nominee, Mario C. Compean, and two other minor candidates shared 18,942 ballots. The more liberal Hill, who had also once been the appointed Secretary of State of Texas, had defeated Briscoe in the primary.

In winning, Clements achieved victory with 350,158 fewer votes than the 1972 GOP nominee, Henry Grover, who went down to defeat because turnout was much lower in the 1978 off-year election than it had been during the aforementioned presidential election year. The 1972 Texas governor's race was the last to coincide with a presidential election because when the terms went to four years, the gubernatorial elections were also set to coincide with the off years between presidential elections.

Clements ran for reelection in 1982, but he was defeated by Democratic Attorney General Mark Wells White by