Despite topping a Champions League group which included Paris Saint-Germain, AC Milan and Newcastle, Dortmund have won just one of seven league games since October.
Last year's runners-up are already ten points behind leaders Bayer Leverkusen, who play their game in hand on Sunday against Eintracht Frankfurt.
Dortmund coach Edin Terzic lamented his side's poor finishing, saying "we were close today, but we weren't successful and that's very unsatisfying".
Ermedin Demirovic opened the hosts' account after 23 minutes, pushing off a challenge from Nico Schlotterbeck before slotting home.
The Dortmund offender appealed for a foul, but the referee allowed the goal after a VAR review.
"I don't want to comment on refereeing decisions, but all I'll say is we had a different opinion to that of the referee," said Terzic.
Donyell Malen scored for Dortmund shortly after, Niclas Fuellkrug finding the Dutchman with a clever backheeled pass to nutmeg the Augsburg defender.
Dortmund midfielder Julian Brandt had a late chance to claim all three points, but he blasted his injury-time shot straight at Augsburg goalie Finn Dahmen.
Dortmund could finish the weekend in sixth place if Hoffenheim win away at RB Leipzig later on Saturday.
Augsburg boss Jess Thorup, who has lost just once in eight matches since taking over in October, said "today was the best chance for us to see where we stand against the better teams".
"After the game, I told the team we've done well."
Union Berlin, whose inaugural Champions League journey ended at the hands of Real Madrid in the German capital on Tuesday, lost 3-0 at Bochum.
Goals from Takuma Asano, Goncalo Paciencia and a late penalty from Kevin Stoeger earned a comfortable win, extending the gap to the relegation places to six points.
Ten-man Wolfsburg fought to a 1-0 win away at promoted Darmstadt, Croatia midfielder Lovro Majer scoring the only goal.
Wolfsburg fell to ten men midway through the first-half, centre-back Maxence Lacroix seeing red for a last-man foul.
The French defender now been red carded five times in less than 100 games for Wolfsburg -- and has more red cards than any other Wolfsburg player.
Elsewhere, promoted Heidenheim won 1-0 at Mainz thanks to an early goal from Marvin Pieringer, leaving the floundering hosts stuck in the bottom two.
The remainder of the top four are in action on Sunday, with second-placed Bayern Munich hosting third-placed Stuttgart, while leaders Leverkusen are at home to Frankfurt.
