After a somewhat off 1967, where he led the AL with 37 doubles and finished in the top 10 in batting average, slugging percentage, hits, total bases, RBIs, runs created, extra base hits, and intentional walks, Oliva's rebound in 1968 was cut short by injury. Missing the last 34 games, he once again hit .289, but so depressed were batting averages it was good for third in the AL by a single point (and only batting champ Yastrzemski topping .300 by a single point as well). He returned to form in 1969 to again place third in the AL with a .309 batting average, with 24 homers, 101 RBIs, and league leads in hits (197) and doubles (39). He finished third in batting average in the American League in 1970 at .325, with 23 home runs and 107 RBIs. He also led the AL in hits (204) for the fifth time, in doubles (36) for the fourth time, and finished second in MVP voting for the second time, this time to Baltimore's Boog Powell.
Oliva started dating Gordette (DuBois) in the mid-60s. They were married in Hitchcock, South Dakota in 1968 and settled in Bloomington, Minnesota. He currently lives in a house he bought in 1972 and all of his four children live within 10 miles (16 km) of their parents. As of 2011, Oliva also had four grandchildren.