Tabea Wassmuth certainly created nerve in the match when she reduced to 2-3 in extra time, but the Serbs kept out and won the qualifier.
Germany tops Group H, 21 points, with two qualifying rounds left to play - three points ahead of Serbia.
The nine group winners in the European qualifiers go straight to the World Cup.
The two go to the European playoff game, which will be decided by two rounds in October 2022, where two direct places and a place for another intercontinental playoff game, are at stake.