Burnett made his mark in the 1997 German Open by reaching the quarter finals and equalled his best run the following year in the 1998 Grand Prix. In a 1997–98 season dominated by Stephen Hendry, Burnett claimed two victories over the world number one as well as recorded victories over Stephen Lee and Mark Williams. He made his first appearance in the final stages of the World Championship in 1996, when he led Terry Griffiths 5–0 and 9–5 before losing 9–10. His second appearance did not come until 2009, equalling Barry Pinches' record for the longest gap between Crucible appearances.