Bigon started his playing career for his native city team Padova. He made his Serie A debut with SPAL in 1967, but obtained most of his playing triumphs with AC Milan, where he played from 1971 to 1980. He appeared in 218 league matches with AC Milan, scoring 56 goals and winning a Serie A championship in 1979, as well as three Coppa Italia tournaments (1972, 1973, 1977) and a Cup Winners' Cup (1973). Bigon retired from playing football in 1984.
Bigon coached his first team, Reggina, in 1986–1987, then Cesena, in 1987. He coached Cesena until 1989, when he left to coach Napoli, then led by Diego Maradona. He immediately won a Serie A championship, the second in Napoli's history. He then won the Italian Super Cup the same year. He left the club in 1991, after a poor eighth place followed by Maradona's forced farewell to Napoli. He then coached minor clubs such as Lecce (Serie B), Udinese (Serie A, saved from relegation after playoffs) and Ascoli (Serie B). In 1996, he was appointed coach of Swiss team FC Sion, which he led to win Swiss Super League for its second time in history. Bigon then tried an unsuccessful return to Serie A with Perugia. In November 1999 he was appointed coach of Greek club Olympiacos, but was fired on April 10, 2000, despite the first place in the championship table.
After seven years without a job, Bigon made a comeback to football in February 2007, when he was appointed coach of FC Sion, a team he already managed years before.
In August 2008, he become head coach of Slovenian football team Interblock Ljubljana. However, this experience lasted only a very short time, as Bigon left the club on September 2008 by mutual consent with the club due to personal health issues.