Brazilian-born midfielder Jorginho converted the spot-kick after substitute Federico Chiesa earned the late penalty for Italy.
The third-placed match has often been criticised by many as the two nations who couldn't reach the finals, fight for a bronze medal on Saturday before the finals at Moscow.
Belgium have shown the most complete attacking force at the World Cup, though without yet playing a European or South American team.
Driven forward by the speed and insight of Hazard and Kevin De Bruyne, Belgium was up 2-0 at halftime before losing some fluency amid a flurry of substitutions after the break.
The 32-year-old Manchester City center-back, whose career has been blighted by injuries, walked off the field early in the second half of Belgium's 0-0 draw with Portugal on Saturday.
Chelsea had to fight back for a sixth win in its last seven league games after conceding a sloppy goal in the 12th minute.
The 26-year-old Chelsea playmaker who has made 182 appearances for the London club since 2012 also said he is unsure about his future.
Hazard is working his way back to full fitness after sitting out the summer with a broken ankle.
Belgium are the first European team confirmed for the World Cup besides host nation Russia.
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