Two days ago the 28-year-old England international from Leamington Spa had beaten the 1991 champion, Dennis Priestley, 3-1, and he hit the same brilliant vein of form against the unfortunate Anderson.
Beaton opened with the first of five 180s, averaged 32.43 per dart and though he registered with only 12 of 32 doubles attempts, five of those misses came in the final leg when he was on the threshold of victory.
Anderson, 45, from Swindon, did not play badly. He averaged 30.46 but Beaton scored so heavily that the former champion had only 18 shots at doubles, hitting six.
'I had something to prove tonight,' Beaton said. 'Most people thought I was going out to Priestley, I think they thought I was a bit lucky. So there was far more pressure on me tonight but I wasn't really nervous until that last leg. I missed a few doubles but then I hit double six and it was all over.'
Anderson, sporting in defeat, said of Beeton: 'He played brilliantly and hardly gave me a shot. So I've no complaints at all.'
In tomorrow's semi-finals Beaton will meet fifth-seeded Alan Warriner, the male nurse from Lancaster, who beat Australia's Wayne Weening 4-1.
This match did not produce the fireworks of the match between Beaton and Anderson, with Warriner needing only an average of 30.27 per dart for a convincing victory.
Warriner, however, into the last four for the first time, beat Beaton in the semi-finals of the Winmau World Masters in London only last month and, as the joint world No 3, will probably start favourite to beat his rival again.
EMBASSY WORLD PROFESSIONAL CHAMPIONSHIP (Frimley Green): Quarter-finals (GB unless stated): S Beaton bt B Anderson 4-1; Alan Warriner bt W Weening (Aus) 4-1.