Kevin Volland's sixth goal of the season had the hosts ahead, though they were pegged back by Paul Verhaegh's penalty.
The Sinsheim side dominated proceedings and got a deserved winner through Mark Uth.
Level at the break after brilliant first-half
Hoffenheim began brightly and nearly broke the deadlock within the first minute. Kevin Volland, not for the first time this season, was through on goal inside sixty seconds after Philipp Ochs' pin-point pass. Unfortunately for the hosts, Marwin Hitz came speeding out and made a vital save.
Augsburg were under massive amounts of pressure and almost fell behind to some poor defending, not long after they had been carved open by Ochs and Volland. This time it was a free-kick from Nadiem Amiri that picked out the unmarked Pavel Kaderabeck, though he couldn't direct his header on target.
The visitors finally managed to come forward and came just as close as Hoffenheim to opening the scoring. Alexander Esswein found space on the right to whip in a dangerous cross to the middle, where Caiuby connected just a few yards goal; to his and everyone's amazement, Oliver Baumann produced a stunning acrobatic save.
A breakthrough was inevitable, and it finally came midway through the half. Eduardo Vargas let fly from 25 yards, only to see his swerving shot cannon back off the post. Augsburg could count themselves unlucky, though, as the ball hit off Hitz and fell kindly to Ochs; he squared for Volland, who gleefully tapped in the opening goal.
Ja-Cheol Koo very nearly gave the visitors a leveler with a stunning 30-yard strike that rose just over the bar at the final moment. Despite this, Markus Weinzierl's men would, controversially, level before the break. A sweetly-struck half volley from Esswein caught Niklas Süle's arms by his stomach, though Guido Winkmann judged that he had deliberately handled the ball. Hoffenheim's protests fell on deaf ears, as Paul Verhaegh sent Baumann the wrong way.
Uth the hero once again
The second half was a real struggle for Augsburg, who lost all of their late momentum from the first-half. Hoffenheim laid siege to their defence and Hitz, who made several top stops low to his left. Amiri and Volland were just two of the players he denied, as the 'keeper and the latter clashed afterwards in a brief moment of frustration.
Eventually, however, the pressure would pay off. A quick, long throw in found Andrej Kramaric darted down the line. He used all his pace and trickery to find space to dig out a cross, though he did more than that and picked out Mark Uth in the area. He scored his fourth goal since the return action after the winter break with a first-time finish that had power and precision in abundance.
Raul Bobadilla came mere inches from turning joy into despair, as he headed narrowly past the far post with a flicked header. That was all Augsburg could muster in reply, as Hoffenheim calmly negotiated the final 10 minutes to secure a vital win. They are now just three points from safety, with Nagelsmann continuing to work his magic. Augsburg are now just four points above their opponents, but should have enough quality to secure their spot in the Bundesliga next year.