Originally signed as a free agent by the Dodgers in 1961, Billingham was groomed as a reliever in the Los Angeles farm system, reaching the major leagues in 1968. Despite a good season (50 games, 3–0 record, 8 saves, 2.14 ERA), the Dodgers left Billingham unprotected in the expansion draft and he was selected by the Montreal Expos, though he would never pitch for them. 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 (52 games, 6–7 record, 4.25 ERA). In 1970 he was moved into the starting rotation (46 games, 24 starts), before becoming exclusively a starting pitcher in 1971.
On April 4, 1974, Billingham gave up Hank Aaron's 714th career home run, which tied Aaron with Babe Ruth for #1 on the all-time home run list at the time.
For his career, Billingham went 145–113 with a 3.83 ERA and 1,141 strikeouts in 2,230.2 innings.