Oliver made the majors for good in1969, having been selected by the Kansas City Royals in the previous October's expansion draft. Playing on a young team that also included fellow rookies Pat Kelly and Lou Piniella (the eventual American League Rookie of the Year), Oliver batted .254 with 13 home runs and 43 in 118 games played. That year, Oliver achieved two firsts in Royal history: 1) He was the first Royal to collect six hits in a nine-inning game with a 6-for-6 performance in a May 4 victory over the California Angels, and 2) he hit the Royals' first-ever grand slam, the shot coming off Jim Bouton in the first game of a July 4 doubleheader against the American League's other 1969 expansion team, the Seattle Pilots.
1970 was a breakout year for Oliver; he established career highs in home runs (27) and RBIs (99) and runs scored (83). He enjoyed two more solid seasons in 1972 (during which he was traded to the California Angels), batting .269 with 20 home runs and 76 RBI, and 1973, batting .265 with 18 home runs and 89 RBI while splitting his time as a utility player. The Baltimore Orioles acquired Oliver for the 1974 stretch drive, he appeared in nine games for Baltimore. During the 1974 his contract was purchased by the New York Yankees. In his career, Oliver batted .256 with 94 home runs and 419 runs batted in, in 847 games played.
Oliver's son Darren is currently a relief pitcher with the Texas Rangers.
Oliver managed the Sacramento Steelheads in 1999. He has also worked at two baseball schools in California's Sacramento County: operating his own Baseball Academy in Sacramento, as well as working as a hitting instructor at Dusty Baker's Baseball Camp in Rancho Cordova.