Liverpool booked their place in the Europa League last 16, whilst Augsburg's dreams came crashing down, as James Milner's early penalty at Anfield gave the hosts a 1-0 win on the night and on aggregate.
With their star man Raul Bobadilla, who injured his hamstring early on in the first leg, restricted to a place on the bench, Augsburg boss Markus Weinzierl opted for Caiuby up front in the hope that the Brazilian would cause the Reds problems.
Jürgen Klopp picked a fairly strong team himself, going for a full-strength XI that contained Philippe Coutinho, Roberto Firmino and Daniel Sturridge, despite having a cup final to compete in on Sunday.
Augsburg behind after dramatic opening five minutes
It was Caiuby who would have the first opportunity of the match, using his pace to get behind makeshift centre-back Lucas Leiva, before the game was even a minute in. He seemed to buckle under the pressure though, sending a powerful effort high over Simon Mignolet's goal.
Things got worse very quickly for the German side though, as they conceded a penalty after three and a half minutes. The hosts played a quick corner, which was crossed by Jordan Henderson and handled by Dominik Kohr, who was bundled into by his own teammate Caiuby. Marwin Hitz dived the right way to try and stop Milner's penalty, but it was a fantastic one that crashed into the bottom right corner.
Reds dominant for the rest of the first half
Liverpool's high pressing style was troubling Augsburg, and the lead was very nearly doubled through Coutinho. Goalscorer Milner won it back, allowing Sturridge and Coutinho to link up in the area, the latter stabbing a shot at Hitz.
Kostas Stafylidis forced Mignolet into action with a long range effort, but was in the book a minute later, carded for pulling Firmino back. The Brazilian would test Hitz soon after, flashing a foot at Alberto Moreno's low cross, the Augsburg 'keeper equal to it.
Firmino's countryman Coutinho continued to threaten, setting up Lucas in the area before having a shot on target himself, but Augsburg were just about keeping themselves in the tie as the first half edged to a close.
It was then, where Augsburg had a golden opportunity to level things up, and take the lead in the tie. Lucas' under-hit backpass to Mignolet was intercepted by Caiuby, who rounded the 'keeper, before hitting a soft shot into the path of a covering Mamadou Sakho.
Hitz was forced into action soon after, Coutinho again causing problems. He got behind the defence after Emre Can played a lovely reverse pass, eventually cutting it back for Sturridge, who had a curling effort pushed wide by the 'keeper.
No second goal as Augsburg frustrate hosts
Sturridge went close again after the game resumed for the second half, capitalising on a sloppy clearance from Hitz to burst through on goal, only for his right foot shoted to slide wide.
The half-time interval seemingly hadn't done Augsburg any favours, as they continued on the back-foot, whilst Liverpool continued to frustrate going forward, Coutinho's curled strike nipping around the post on the hour mark.
Bobadilla eventually entered the fray, getting the last 20 minutes, but not until Augsburg had another chance to level the tie. The ball was in a fairly ordinary looking place in midfield, but suddenly the Liverpool defence was out of shape, leaving Werner through on goal after the ball was played into him. However, Mignolet reacted quickly to come off his line, saving with his feet.
Divock Origi's ball in seconds later flew off the feet of Kohr, but Hitz was again fantastic, saving well before Coutinho's follow up was blocked. It was like groundhog day at Anfield, Hitz at it again to block Henderson's effort from within the six yard box after Firmino's lay-off.
Bavarians miss chance to cause late twist
As long as Augsburg stayed in the game, you had a feeling that they'd get at least one final opportinity to level things up, and went close to squaring it with four minutes left on the clock, as a cut back into the area fell for Bobadilla, only for Milner to nip across and clear.
They got another though, Lucas conceding a silly free-kick on the edge of the area in the dying minutes. Stafylidis stepped up, threatening with a well executed set-piece, that had Liverpool hearts in mouths as it curled narrowly wide.
Five minutes of additional time was then announced, further increasing the pressure on the hosts, giving Augsburg more hope of nicking it. However, the Reds started to play smarter, keeping it in the corner to waste time, and they edged through - bringing Augsburg's European campaign to an end.