Zlatko Junuzovic was on target in the 34th minute and set up fellow countryman Florian Grillitsch with a well-planned free kick move just before the hour.
Substitute Florian Kainz netted the third goal two minutes after coming on in the 88th minute as the former German champions moved up to 13th place, three points clear of the relegation playoff spot.
It was another miserable afternoon for promoted Leipzig, who had taken the Bundesliga by storm earlier this season but have now managed just two wins in seven games.
They remain second on 49 points, with leaders Bayern Munich, 10 points clear, facing Borussia Moenchengladbach on Sunday.
"We seem to be a bit unlucky at the moment," Leipzig coach Ralph Hasenhuettl told reporters.
"What is important now is to use the break for international matches to fill up on power for the difficult work ahead of us."
Third-placed Dortmund closed to within three points of Leipzig after their lacklustre 1-0 win over Ingolstadt on Friday.
Leipzig's Emil Forsberg should have done better in the 26th but his low drive sailed narrowly wide of Felix Wiedwald's goal.
Read the full article on eurosport.co.uk: Hoffenheim edge into fourth after Wagner goal