Bayern completed the double thanks to Robben's outstanding display with two assists and a goal.
Robert Lewandowski and Arjen Robben combined for all three goals as Bundesliga leaders Bayern Munich eased to an impressive 3-1 victory for their second win over Augsburg this week.
Having also beaten their Bavarian neighbours by the same margin on Wednesday at home in the German Cup, Bayern completed the double thanks to Robben's outstanding display with two assists and a goal.
"Robben and Lewandoski played very well and were a good combination," said Bayern coach Carlo Ancelotti.
"When quality players play together like that, it's really good for the team."
Bayern took the lead at Augsburg's WWK Arena when Robben's pass found Lewandowski unmarked to rifle home his first Bundesliga goal for six weeks on 19 minutes.
The Poland hot-shot returned the favour two minutes later.
His shot was parried by Augsburg goalkeeper Marvin Hitz, but Lewandowski spotted Robben unmarked and the Dutchman drilled home the pass.
Just after the break, Robben snapped up a disastrous pass from Augsburg's Gojko Kacar to thread a pass for Lewandowski to fire home on 48 minutes for his seventh goal in nine league games.
"We played well from the first minute and controlled the whole game," said Lewandowski. "I was happy to score again."
Just as they did in the cup, Augsburg pulled a goal back when Koo Ja-Cheol tapped home Daniel Baier's pass after Bayern centre-back Mats Hummels' failed clearance on 67 minutes.
Robben was taken with 14 minutes to go, but Ancelotti said he should be available to play at Eindhoven in the Champions League on Tuesday.
This was Augsburg's third straight loss in all competitions to leave them just above the relegation places.
Munich are two points clear in the table, but second-placed Leipzig kept up the pressure with a 2-0 win at Darmstadt as Marcel Sabitzer scored both goals.
Leipzig are nine games unbeaten on their debut season in Germany's top flight -- just one short of the record for a promoted team.
Borussia Dortmund are winless in their last four league games after Saturday night's goalless draw at home to rivals Schalke in the Ruhr derby.
It was a frustrating night for Dortmund as Ousmane Dembele hit the crossbar, then had a shot saved, while Pierre-Emerick Aubameyang and Mario Goetze also went close in the second half.
However, Dortmund have extended the club record of 26 league matches unbeaten since Bayern beat them at home in April 2015 and are fifth in the table while Schalke are 12th.
Freiburg's 3-1 win at Werder Bremen, thanks to goals by Maximilian Philipp, a Vincenzo Grifo penalty and a strike by Albanian international Amir Abrashi, left them eighth.
Defender Santiago Garcia pulled a second-half goal back for Bremen, but the defeat leaves them 15th, one point from the relegation places.
Bayer Leverkusen warmed up for Wednesday's away Champions League match at Tottenham Hotspur with a 2-1 comeback win at VfL Wolfsburg, who remain in the relegation places.
Wolfsburg, now winless in eight league games, took the lead through Maximilian Arnold, leaving Bayer coach Roger Schmidt fuming in a private box.
The Leverkusen boss was completing his two-match ban for calling Hoffenheim's coach Julian Nagelsmann "a nutter" during last Saturday's 3-0 defeat which saw him banished to the stands.
But Leverkusen roared back with two goals in five second-half minutes by Admir Mehmedi and Tin Jedvaj to give Bayer their first win in five games to go 10th.
Yunus Malli and Levin Oztunali scored in Mainz's 2-0 over second-from-bottom Ingolstadt, who had Max Christiansen sent off late on for a second yellow card.