Robert Lewandowski followed up Wednesday's sensational performance at Wolfsburg with two goals as Bayern Munich earned a comfortable 3-0 win at Mainz.

The 27-year-old striker also celebrated his 100th – and later 101st – Bundesliga goals in just 168 appearances for Bayern Munich and Borussia Dortmund. Bayern's performances in the league this season have followed a consistent trend: the German champions were insipid in the first half before finding their shooting boots after the interval.

With 15 of 20 league goals this season scored in the second half, there was a sense of inevitability when Lewandowski scored twice in 13 minutes. Kingsley Coman added a decisive third to seal the points with around 30 minutes left to play.

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Pep Guardiola handed Javi Martinez a starting place after his welcome return from injury, leaving Jerome Boateng on the bench. With just the single appearance last year in an injury-ravaged campaign, Martinez returned to the side in midweek against Wolfsburg and lasted about 67 minutes at the Coface Arena.

After a slow start to proceedings, Bayern was awarded a penalty on 19 minutes. French forward Coman showed a great change of pace on the right-wing and was fouled by Pablo de Blasis. But Thomas Müller lost his footing from 12 yards, blazing his spot-kick uncharacteristically over the crossbar.

Mainz's stoic defensive performance was admirable, and the penalty will have been a disappointment for head coach Martin Schmidt. Eight minutes later after Müller's miss, the Carnival Club should have gone ahead when Yoshinori Muto carved out a few yards of space to fire a shot at goal, but the Japanese striker missed the target from around 10 yards out.

Douglas Costa then brought out a wonderful save from Loris Karius on 33 minutes, the Brazilian sprinting clear of the midfield pack and blasting a corker of a shot from 30 yards, which was heading for the top corner. Karius reacted well, tipping the ball over his own crossbar.

Guardiola showed trust in his starting eleven by making no changes at the break. Bayern Munich found an extra gear and Lewandowski continued where he had left off in midweek with the opening goal for the champions. The cross was supplied by Coman as Lewandowski cleverly peeled away from Stefan Bell before heading accurately into the corner.

Thirteen minutes later, the Polish hitman made it 10 for the season, rounding Karius and sliding the ball gleefully into an empty net. Bayern's 100% record was just about wrapped up ahead of the clash with Borussia Dortmund next week, but there was more scoring on 68 minutes.

Costa cruised past his markers on the left, crossing at the byline and Coman drifted in from the right-flank to score Bayern's third of a comfortable afternoon in Mainz.

Meanwhile, Andre Schubert made it two wins from two as Borussia Mönchengladbach coach as the Foals beat Stuttgart 3-1.

Schubert, who is the interim successor of Lucien Favre, watched his side thrash Augsburg in midweek before starting positively in Stuttgart. Granit Xhaka headed in the opener on 17 minutes and soon after Christian Gentner headed into his own net to send the away side into a 2-0 lead.

Daniel Ginczek scored from the penalty spot on 41 minutes, a deserved reward for Stuttgart's dangerous attacking play. Yet it was the team's defensive frailties which punished Alexander Zorniger's side again as Raffael beat the offside trap to score Gladbach's third of the game and secure a second win in successive games.

Bayer Leverkusen earned a comfortable 3-0 at Werder Bremen ahead of a Champions League trip to Barcelona in midweek.

Werder was without US international Aron Johannsson who has been struggling with injury this week. Admir Mehmedi opened the scoring on the half hour mark, his shot taking a wicked deflection against Assani Lukimya.

Julian Brandt and Kevin Kampl scored two goals in eight minutes midway through the second half to secure back-to-back wins for Roger Schmidt's men after ending a four-game winless streak on Wednesday.

Hoffenheim picked up three points for the first time this season with Kevin Volland scoring a double in a 3-1 win at FC Augsburg.

On nine minutes, Germany international Volland burst inside from the right, all-left-foot, then rifled a shot into the bottom corner. Hoffenheim has shown a penchant this season for losing concentration in matches and this one in Augsburg was certainly going in the same direction.

Halil Altintop struck the crossbar on 29 minutes before Markus Weinzerl's side equalized eight minutes later through Ja-Cheol Koo. The South Korean had the easiest of finishes inside the six-yard box following a mistake from Oliver Baumann. But Volland and Jonathan Schmid scored late on to send Hoffenheim out of the relegation zone.

Hannover's Hiroshi Kiyotake cancelled out Bas Dost's opener to secure a point at Wolfsburg, but it fails to stop Michael Frontzeck's side from slipping to the bottom of the table.