Lewandowski showed great footwork to evade Dominik Kohr and slot in the opening goal after 15 minutes.
He then ran on to Thiago's perfectly weighted pass to score his 31st Bayern goal of the season on the hour mark.
Thomas Muller drove in a third from eight yards before Raul Bobadilla scored late on for Augsburg, Liverpool's Europa League opponents.
Victory was the perfect response from Pep Guardiola's side, after they dropped league points for only the third time all season in drawing 0-0 at Bayer Leverkusen last weekend.
Bayern's players wore T-shirts as they walked out before kick-off in support of defender Holger Badstuber, who suffered the latest in a series of injury setbacks when he broke his ankle in training on Saturday.
The win ensured they remain comfortably clear of second-placed Borussia Dortmund, who beat Hannover 1-0 on Saturday.
Augsburg, who host Jurgen Klopp's Reds in Thursday's round of 32 first leg, are one point above the relegation play-off place after back-to-back league defeats.
Elsewhere, mid-table Hamburg ended a six-match run without a league win by coming from a goal down to earn a 3-2 win over Borussia Monchengladbach, who missed the chance to climb into the top four.
Fabian Johnson gave the visitors the lead, but they trailed at half-time after Martin Hinteregger deflected Gideon Jung's shot into his own net, and Artjoms Rudnevs scored only his second goal of the season.
Substitute Ivo Ilicevic made it 3-1 to Hamburg with 11 minutes left, and Raffael's late goal for Gladbach was not enough to spark a late comeback.
Two Robert Lewandowski goals helped restore Bayern Munich's eight-point Bundesliga lead as they beat Augsburg.