Burnett defeated thirteenth seed Les Gillett at Potters in Norfolk
Scotland's Stewart Anderson and Darren Burnett continued the cull of seeds at the world indoor bowls in Norfolk.
Qualifier Anderson defeated 15th seed Mark McMahon of Australia 8-6 11-5, while unseeded Burnett knocked out 13th seed Les Gillett (England) 11-2, 8-3.
But fifth seed Greg Harlow of England had no trouble beating Welsh qualifier Phil Rowlands 7-2 8-7 in round two.
And Scotland's world number one Alex Marshall, seeded two, knocked out English qualifier Tim Stone 10-6 7-3.
Marshall, the 42-year-old who has won the title a record five times, said: "I can't see why I can't win it again if I play like that."
Stewart played phenomenal bowls this morning and could certainly go on and win the title
But it was 24-year-old Anderson who has become an outside tip for the title and now stands between Marshall and a place in the quarter-finals.
Anderson, the world junior champion from Cumnock, sprung to prominence when reaching the semi-finals of last month's Scottish International Open as a qualifier.
"Stewart is a fantastic prospect - he was excellent today," said Marshall. "He doesn't seem to fear anybody."
McMahon, the 2004 runner-up, was making his last appearance after announcing his retirement before the match and said that Anderson could be a surprise winner.
"Stewart played phenomenal bowls this morning and could certainly go on and win the title," he said.
Six seeds, including top seed and reigning champion Billy Jackson, had already fallen before the wins by Anderson and Burnett.
Burnett, the 33-year-old from Arbroath, recorded his victory only two weeks after suffering Swine Flu and, as the world number 17, now has a chance of moving into the top 16.