Bayern boss Pep Guardiola fielded a much-changed line-up on Saturday, seemingly with one eye on the second leg of his side's UEFA Champions League quarter-final against Manchester United in midweek.
The result was a disjointed display from the visitors, with Manuel Neuer already established as the busiest goalkeeper by the time Sascha Molders slotted home his first Bundesliga goal since October to decide the contest in the 31st minute.
Augsburg remain eighth in the table, five points shy of a UEFA Europa League qualification place, and closed the gap on Mainz directly above them.
Thomas Tuchel's side were beaten 2-0 by rivals Eintracht Frankfurt at the Commerzbank-Arena, with Joselu and Alexander Meier on target in the second half.
The scoreline was the same in the relegation six-pointer at Stuttgart, where the hosts responded to Hamburg's 2-1 win over Bayer Leverkusen on Friday by overcoming Freiburg.
Alexandru Maxim and Martin Harnik were on target to lift Stuttgart out of the relegation zone and up to fourth-bottom - one place and two points shy of their opponents.
That meant that the big losers in the scrap to remain in the Bundesliga were Nuremberg, who slipped to a 2-0 home defeat against fourth-placed Borussia Monchengladbach and now lie 17th.
Capitalising on Leverkusen's slip-up, a reverse that cost their coach Sami Hyypia his job, Juan Arango ensured Monchengladbach were rewarded for an enterprising start when he found the net with a deflected free-kick.
Josip Drmic rattled the crossbar for Nuremberg before Max Kruse was fouled by Mike Frantz and converted the resulting penalty.
Borussia Dortmund took a step closer to securing second place after Schalke drew 1-1 at Werder Bremen.
Franco Di Santo's second goal in as many games put Bremen ahead before Leon Goretzka drove in a 33rd-minute equaliser, although Schalke were then unable to convert some fine play into a winner.
Dortmund also fell behind as Ivica Olic crowned an impressive first-half display by Wolfsburg at Signal Iduna Park.
Jurgen Klopp's men came roaring back after the interval, however, to secure a 2-1 triumph and move three points clear of Schalke.
Robert Lewandowski equalised in the 51st minute, heading home a corner from Marco Reus, who subsequently capitalised on an error from Wolfsburg goalkeeper Max Grun to complete Dortmund's comeback.
