Crowe's father played in three first-class cricket matches for Canterbury and Wellington between 1953 and 1957.
Crowe began his first-class cricket career at South Australia, where he played from 1977–78 to 1981–82.
Against a fierce fast bowling attack that included Courtney Walsh, Malcolm Marshall and Joel Garner, he scored his second Test century (112); but despite his heroics, New Zealand still lost by 10 wickets.
He also played in 75 ODIs from 1983 to 1990, including the Cricket World Cups in England in 1983 and in India in 1987.
He ran a golfing holiday business in Florida for a period, and since 2004 he has been an ICC match referee, including the World Cup finals in 2007 and 2011.