The result, coupled with Turkey's 3-1 loss to Group A winner Germany, put Belgium in second place ahead of its final game against Germany. Turkey, which is a point behind, is expected to beat Azerbaijan in Tuesday's games.
Belgium was 2-0 ahead by halftime after a penalty by Timmy Simons and a goal from Eden Hazard. Vincent Kompany made it 3-0 shortly after the break before Kazakhstan went down to 10 men when Nurtus Kurgulin was sent off in the 59th.
Substitute Marvin Ogunjimi completed the scoring for the hosts in the 85th. Kazakhstan grabbed a late consolation through Kairat Nurdauletov's penalty.