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.
World Cup semi-finalists Belgium dominated the match with Lukaku putting them ahead just before the half-hour mark after a defensive mix-up before they ran riot after the break.
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 foray of the second half before he set up Batshuayi for the third after Charlie Mulgrew gave the ball away.
Batshuayi netted his second from the edge of the area with Ryan Jack to blame after he lost possession in midfield.
Belgium open their Nations League campaign in Iceland on Tuesday, while Scotland start at home to Albania on Monday.
"The players were well focussed overall and for us it was a good exercise for Tuesday," said Belgium manager Roberto Martinez. "Take the scoreline away, we were very clinical in front of goal."
The gulf in class was shown by the fact that Scotland got their first corner in the 84th minute as they struggled against an experienced Belgium side, who came third at the World Cup.
But it was the home side's mistakes that cost them dear.
"We shot ourselves in the foot," said Scotland manager Alex McLeish. "They’re a top, top team. We were perpetrators of our own downfall. These are errors that should be easily eradicated.
"It was just a catalogue of errors. If anybody’s got to take the blame, it’s me for telling them they have to pass it.
“It was a very difficult encounter against a great team. We strive to get to that level. We’re well away from that ... level."
It was Scotland's fourth defeat in five matches under McLeish, who took over when Gordon Strachan stood down after they failed to qualify for the World Cup.
(Writing by Ken Ferris; Editing by Pritha Sarkar/Peter Rutherford)
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