Three goals in the final six minutes of the first half went a long way to settling the contest as Halil Altintop scored the first for the hosts in the 39th minute, quickly followed by team-mate Tobias Werner three minutes later.
Roberto Firmino responded with a goal for Hoffenheim in the final minute of the first half.
However, after an even second half, Raul Bobadilla struck in stoppage time to put the result beyond doubt and send Augsburg fifth - level on points with Borussia Monchengladbach and Schalke above them.
Hertha Berlin's poor away form continued as they slipped closer to the Bundesliga drop zone following a 2-0 defeat at Werder Bremen.
This latest defeat came courtesy of strikes either side of half-time from former Chelsea striker Franco Di Santo, who moved on to eight goals for the campaign.
Jannik Vestergaard also made his debut for Viktor Skripnik's side, who climb to 12th after their first match since the winter break.
