Dee ihe na-aga n'ihu maka paragraf a - Unser mere IndyCar mbụ ya na 1962 (ewepu agbụrụ Pikes Peak nke bụ akụkụ nke oge IndyCar na 1950s). Ọ gbara ọsọ maka Andy Granatelli n'etiti 1963 na 1965 na injin Novi. Unser gbara ọsọ nke mbụ ya n'Indianapolis 500 n'afọ 1963. Ọ dara n'oge ma nọrọ n'ọkwa nke 33. Unser nke abụọ Indianapolis 500 na 1964
kwụsịrị n'agba nke abụọ n'ihe mberede nke gburu Eddie Sachs na Dave MacDonald. Unser kwagara IndyCar nke Bob Willke nwere site na 1966 ruo 1970. Mmeri IndyCar mbụ ya bịara na 1967 na Mosport, na Ontario. Otu afọ mgbe nke ahụ gasịrị, Unser meriri Indianapolis 500 nke mbụ ya, na-etinye ihe ndekọ dị ka onye ọkwọ ụgbọala mbụ na-agba ọsọ karịa kilomita 170 kwa elekere na Indianapolis. N'afọ 1968, Unser na onye isi ndị ọrụ Jud Phillips rụkọrọ ọrụ wee merie USAC National Driving Championship mbụ ya na mmeri na Stardust International Raceway, Phoenix Raceway, Trenton Speedway, Indy, na Pikes Peak Hill Climb.