Belgium's best chance in the first half fell to new Manchester City man Kevin De Bruyne
Belgium narrowly defeated Cyprus in Nicosia to keep Group B leaders Wales waiting to qualify for Euro 2016.
The Welsh drew 0-0 with Israel in Cardiff and would have qualified if Belgium had failed to win.
But Chelsea forward Eden Hazard hit the winner four minutes from time, stroking in Dries Mertens's cutback.
Earlier, midfielder Kevin De Bruyne had struck straight at the goalkeeper when through on goal and Marios Nikolaou had a low effort saved by Thibaut Courtois.
Wales need a draw away at Bosnia-Herzegovina or at home against Andorra to secure qualification, while Belgium also have a chance to qualify automatically when they face Andorra and Israel in their last two matches.
Second-placed Belgium are one point behind Wales with the top two sides securing automatic qualification for the tournament in France next summer.
