He died in his car Saturday outside a local fast-food restaurant. Local medical authorities said alcohol poisoning was the cause of death.
Bessent played for the Dodgers from 1955 to 1958, moving with them to Los Angeles in his last year in the major leagues.
He was best remembered for his World Series performances, pitching against the New York Yankees in five series games in 1955 and 1956. He was 1-0 with a 1.35 earned-run average in 13 1/2 innings.
Bessent, who grew up in Jacksonville, was called up to the Dodgers from their Triple A farm club in St. Paul, Minn., in 1955, at the same time as Roger Craig. Both rookies pitched complete game victories in a double-header against the Pittsburgh Pirates.
Bessent finished his big league career with a 14-7 record, 3.33 ERA and 12 saves.
He teamed with Clem Labine and Ed Roebuck to form one of the top relief staffs of the period.
"He had what was called a heavy pitch. Catchers didn't want to catch him because he threw so hard," Labine said Monday from his home in Woonsocket, R.I.
Bessent developed arm trouble in 1959 and retired in 1962 after four seasons in the minors.