Unsworth is best remembered for his time at Everton during the 1990s, where he was part of their FA Cup-winning team of 1995 and acquired the nickname "Rhino". He earned one full England cap in 1995. He also played in the Premier League for West Ham United, Portsmouth, Sheffield United and Wigan Athletic, and in the Football League for Ipswich Town, Burnley and Huddersfield Town.