Christian Benteke opened the Belgians’ account before Yannick Carrasco and Thorgan Hazard completed the job. Estonia’s consolation goal came from Erik Sorga.
The Netherlands threw away a 2-0 lead to draw 2-2 with Montenegro in Podgorica, meaning the Dutch still have to get a result against Norway on Tuesday to reach their first World Cup finals since 2014.
The Dutch are top of Group G with 20 points while Turkey have 18 points, the same total as Norway.
The Turks face Montenegro in their final game.