From 1959 to 1971 Winkles was the ASU Sun Devil baseball program's first varsity head coach. His overall record while head coach at ASU was 524–173, a winning percentage of .751, and he led ASU to its first three national titles (1965, 1967 and 1969). He also coached several notable players while he was at the helm of the Sun Devils, including Rick Monday, Sal Bando, Reggie Jackson, Sterling Slaughter and Larry Gura. Winkles was named the 1965 and 1969 NCAA Coach of the Year and The Sporting News Coach of the Year in 1965, 1967 and 1969. Winkles was inducted into the ABCA Collegiate Baseball Hall of Fame in 1997. His No. 1 jersey was honored at Packard Stadium and the field was named in his honor.
On June 26, Winkles returned to the Athletics to manage Oakland for parts of the 1977 and 1978 seasons, as he replaced (in 1977) and then was succeeded by (in 1978) the same manager: Jack McKeon. The A's were then a struggling outfit in the final throes of the Charlie Finley era. But Winkles' 1978 team roared to a 19–5 start by May 5, and was still 24–15 after sweeping a doubleheader against the White Sox on May 21 when Winkles resigned two days later on May 23 despite the club being in first place in the American League West.[3] The primary reason behind his resignation was Finley's micro-management style.[4] By extension, he had also grown tired of Finley's hand-picked vice president Stanley Burrell.[5] His final managerial record: 170 wins, 213 defeats (.444).
A coaching stint with the White Sox immediately followed Winkles' 1978 resignation as the A's manager, and he was a member of the White Sox staff through 1981. Then, from 1982 to 1985, Winkles led the Chisox' player development department. He joined the Montreal Expos as a coach from 1986 through 1988, and then moved into the broadcast booth as an analyst on the Expos' radio network from 1989 through 1993. In 2006, he was inducted into the College Baseball Hall of Fame.