A James Milner penalty in the 5th minute was enough to send Liverpool through to the Europa League last 16 at Augsburg's expense.
However, the job was completed, just, without too much damage - and the need for energy-sapping extra-time - to allow Jurgen Klopp and his players to concentrate on Sunday's League Cup final against Manchester City.
Aside from the result the real positive was another 65 minutes in the bank for Daniel Sturridge, making his third consecutive start for the first time since last March, who looked Liverpool's most dangerous player and will be the key man again at Wembley.
Even before kick-off the numbers were loaded in Liverpool's favour as they had played German opposition 16 times at Anfield and never lost, winning 13 matches and keeping 12 clean sheets.
But those figures hardly added up to much in the context of a game which became increasingly tense with such a slender lead.
Following a scare after just 46 seconds when Caiuby fired over after being given a free run through, the hosts settled into their stride and were ahead by the fifth minute.
Dominik Kohr and Caiuby got themselves in a tangle trying to deal with Jordan Henderson's cross resulting in the former handling.
Milner tucked the penalty inside Marwin Hitz's left-hand post and just out of the reach of the goalkeeper for his second successive spot-kick in home European games.
Liverpool's attacking trio of Sturridge, Philippe Coutinho and Roberto Firmino were displaying a greater understanding of each other on their third consecutive start together and that caused Augsburg plenty of problems in the final third.
It was only the smart reactions of Hitz which kept the score to 1-0 at half-time as he saved from Coutinho, brilliantly tipped over Firmino's deflection and denied Sturridge at the same near post with another outstanding low stop.
But despite their dominance there was the occasional concern at the other end with Simon Mignolet palming away left-back Kostas Stafylidis' shot and Caiuby rolling a shot wide having rounded the goalkeeper from a short backpass by midfielder-turned-centre-back Lucas Leiva.
Sturridge should have put the game beyond Augsburg just after the break when a misplaced pass by Christoph Janker was returned by Coutinho but, having side-stepped Ragnar Klavan, he rolled a right-footed shot wide of the far post.
It was his last meaningful action as Divock Origi replaced him just after the hour but, with Augsburg sensing their chance, Mignolet had one dash to the edge of his area to beat Tobias Werner to a dangerous through-ball.
Hitz's superb reactions were tested again when Origi's cross was deflected at him by team-mate Halil Altintop and then Henderson stabbed the ball at him from seven yards.
The final 10 minutes was the most nervy of affairs as, after substitute Jan Moravek volleyed wide, the majority of the hearts inside Anfield skipped a beat as Stafylidis's 89th-minute free-kick dropped just over the crossbar.
Having fallen at this hurdle on their last two attempts, the latest 12 months ago in a penalty shoot-out against Besiktas, progress has at least been made.