Billingham was born in Orlando, Florida and graduated from Winter Park High School in 1961. He believes that he is a distant cousin of Baseball Hall of Fame member Christy Mathewson although, the exact relationship is not known. He was signed by the Los Angeles Dodgers as an amateur free agent on June 12, 1961. He spent seven years in the Dodgers’ minor-league system, where he was groomed as a relief pitcher. Billingham made his major league debut with the Dodgers on April 11, 1968 at the age of 25. He didn't give up a run until his seventh appearance as a relief pitcher for the Dodgers. In his only appearance as a starting pitcher, he shut out the Pirates through eight innings. Billingham finished the season with a 3-0 win-loss record with a 2.14 earned-run average however, the Dodgers left Billingham unprotected and he was selected by the Montreal Expos in the 1968 Major League Baseball expansion draft. In January 1969, the Expos traded Donn Clendenon to the Houston Astros for Rusty Staub. Clendenon refused to report, and Billingham was later sent to Houston to complete the trade. In 1969, Billingham was again used as a reliever. In 1970 he was moved into the starting rotation, before becoming exclusively a starting pitcher in 1971. On November 29, 1971, Billingham was involved in one of the most significant trades in the history of the Cincinnati Reds when he was acquired from the Astros along with Ed Armbrister, Cesar Geronimo, Denis Menke and Joe Morgan. The trade helped to transform the Reds into the into the juggernaut known as the Big Red Machine that would dominate the National League for the next five seasons. Billingham's best season was 1973, going 19-10 with a career-best 3.04 ERA. He led the National League with 40 starts, 293 innings pitched and seven shutouts and earned a berth on the National League All-Star team in the 1973 All-Star Game. He followed that with a 19-11 season in 1974. On April 4, 1974, Billingham gave up Hank Aaron's 714th career home run, which tied Aaron with Babe Ruth for No. 1 on the all-time home run list at the time. Billingham was one of the most effective pitchers in World Series history. In the 1975 World Series, he was the starting pitcher for Cincinnati in their Game 2 victory where, he gave up a first-inning run before holding the Boston Red Sox scoreless for the next four innings. His scoreless streak continued in Game 6 where he appeared as a relief pitcher and allowed one hit in one inning pitched. In the climactic Game 7, Billingham entered the game in the bottom of the fifth inning as a relief pitcher with the Reds trailing the Red Sox by a score of 3-0. He held the Red Sox scoreless for two innings, allowing the Reds to come from behind to take a 4-3 victory and clinch the 1975 World Series championship. In seven games for Cincinnati, he went 2–0 with a 0.36 ERA, allowing just one earned run in 25 innings pitched. In 1979, he posted a 10-9 record with the Detroit Tigers to finish his tenth consecutive season of ten or more wins.
Career statistics
In a 13-season major league career, Billingham posted a 145-113 record with 1,141 strikeouts and a 3.83 earned run average in 2,231.1 innings pitched, including 27 shutouts and 74 complete games. He posted a 1.93 earned run average in 42 innings of postseason pitching.