Second-half goals from Christian Benteke and Vincent Kompany secured the result against a Scotland that, despite offering little in the game, had somehow managed to hold out until 65 minutes against the Belgian attack.
It was attack versus defence from the first whistle, with Allen MacGregor being forced into a string of saves to keep his side in the game as Belgium dribbled and passed their way around a static Scottish defence with ease. The keeper was called into action to deny the lively Dries Mertens twice, and also had to rush out to save at Nacer Chadli's feet.
Dries Mertens proved not only a goal threat, but also a major source of creativity for the Belgians, and they should have opened the scoring much earlier when he set up Benteke in a good position, but the Aston Villa striker failed to react quickly enough to turn the ball home.
Scotland offered little throughout the half, but somehow came close to scoring twice: a pair of well-struck Shaun Maloney free-kicks tested Thibaut Courtois, but the Belgian keeper proved himself worthy, doing well to save both efforts. Thanks to him and his opposite number MacGregor, the teams went in at half-time with the score at 0-0.
The second half continued much the same way as the first, but the introduction of Eden Hazard proved decisive for the home side. The Chelsea playmaker's passing was crucial to helping Belgium unlock the massed Scottish defence, as his trickery opened them up even more than they had been previously.
Eventually, the Scots' defence could hold out no longer. A simple move found the breakthrough in the end, Kevin de Bruyne crossing from the left to find an unmarked Christian Benteke at the far post, who nodded past MacGregor's despairing dive.
Before the Scots could think about mounting a comeback, however, it was 2-0 and game over as Vincent Kompany picked up the ball outside the Scotland area and curled a superb shot into the near post.
The result leaves Scotland's slim hopes of qualification dashed, and it's likely that Craig Levein's time is up in charge of Scotland. There had been calls from official supporters groups for his dismissal before the game, and neither the performance or the result will have done anything to change their views. For Belgium, they are beginning to look like the great side they potentially could be, particularly if Eden Hazard is playing at his best - without him, they dominated play but lacked a cutting edge. With him in the side, they look to be capable of anything.