Romelu Lukaku and Eden Hazard had put the visitors on top in the Nations League warm-up as the Scots suffered their heaviest home reverse since February 1973, when they lost 5-0 to England.
Scotland gifted the visitors the first goal when goalkeeper Craig Gordon rolled the ball to John McGinn who was dispossessed by Mousa Dembele before Dries Mertens set up Lukaku to score.
Hazard made it 2-0 with some trickery and a fierce drive in Belgium's first second-half foray before he set up Batshuayi for the third after Charlie Mulgrew gave the ball away.
The gulf in class was shown by the fact that Scotland only earned their first corner in the 84th minute against Roberto Martinez's experienced side, who came third at the World Cup.
It was Scotland's fourth defeat in five matches under Alex McLeish, who took over when Gordon Strachan stood down after they failed to qualify for the World Cup.
Belgium open their Nations league campaign away to Iceland on Tuesday, while Scotland start at home to Albania on Monday.