Fazio attended Santa Clara University, threw and batted right-handed, stood 5 feet 7 inches (1.70 m) tall and weighed 165 pounds (75 kg).

[1] Fazio signed with the Colt .45s and split his first professional season, 1962, between Houston's first-ever National League team and its Triple-A affiliate, the Oklahoma City 89ers.

He hit both of his major league home runs in that year, off lefthanders Denny Lemaster and Hall of Famer Warren Spahn of the Milwaukee Braves.

After the 1965 season, he was the "player to be named later" in an earlier trade that sent Houston pitcher Jesse Hickman to the Athletics for slugger Jim Gentile.

Despite his small stature, Fazio had shown power that year by hitting 23 home runs for Oklahoma City.