As the Dodgers' leadoff hitter for most of the 1950s, he scored over 100 runs in each of his first four seasons and led the National League in triples in 1953 and walks in 1959.

Born in Nashville, Tennessee, Gilliam began playing on a local semi-pro team at age 14 and dropped out of high school in his senior year to pursue his baseball career.

In 1951, he was signed as an amateur free agent by the Brooklyn Dodgers, who sent him to play for their Triple-A International League farm team, the Montreal Royals; he could not play for the Dodgers' Double-A affiliate, the Fort Worth Cats, as blacks were still barred from the Texas League.

On July 21 of that year, he tied John Montgomery Ward's 1892 major league record of 12 assists in a game.

In the Dodgers' last season in Brooklyn in 1957, he batted .250 but led the National League in putouts and fielding percentage and again finished second behind Mays in stolen bases.

On September 5, Gilliam hit a 2-run pinch triple in a road game against the Houston Astros, giving the Dodgers a 3–2 lead in the ninth inning; the Los Angeles Rams, playing a preseason game against the Philadelphia Eagles at the Coliseum, were playing so poorly despite their 10–0 win that the biggest cheer from the stands came from people listening to portable radios tuned to the Dodger game who cheered when Gilliam got the hit.

In the 1953 World Series he singled to lead off Game 1, and had a solo homer in the fifth inning batting left-handed.

In the 1963 World Series, he scored the only run of Game 3 in the first inning, after walking and advancing to second base on a wild pitch; after advancing all the way to third base on an error by Joe Pepitone in the seventh inning of Game 4, he scored on a Willie Davis sacrifice fly to give the Dodgers a 2–1 win and a Series sweep.

Gilliam suffered a massive brain hemorrhage at his home on September 15, 1978, and, following surgery, lapsed into a coma from which he did not recover.

His uniform number 19 was retired by the Dodgers two days after his death, prior to Game 1 of the 1978 World Series.

The Dodgers wore a black memorial patch with Gilliam's number 19 on the left sleeve of their jerseys during the 1978 World Series, won by the archrival New York Yankees in six games.