Carrasco took advantage of poor defending to give Belgium an early lead but the hosts were unable to increase their advantage with a virtual second-string side.
Serbia did much the same as they prepared for their last Group G qualifier against Bulgaria on Sunday in which a home win would see them through.
Wednesday's clash was moved to the Den Dreef Stadium in Leuven from Brussels on Tuesday after heavy rainfall left the pitch at the King Baudouin Stadium unplayable.
No spectators were allowed as officials said there had not been enough time to arrange adequate security.
Two Swedish supporters were killed by an Islamist militant ahead of a qualifying clash in Brussels last month and the game between Belgium and Sweden was abandoned at half-time.
Belgium, who have qualified for the Euro 2024 finals in Germany, complete their campaign at home to Azerbaijan on Sunday.
