Bayern Munich opened up a 10-point gap at the top of the Bundesliga with a clinical 3-0 win over Eintracht Frankfurt.

Robert Lewandowski made it 100 goals in all competitions for the defending champions with a brace either side of Douglas Costa's 41st-minute strike.

Frankfurt asked plenty of questions of their illustrious hosts until Lewandowski's second in the 55th minute effectively ended the contest, with heroic defending from Mats Hummels and rank wastefulness from visiting striker Branimir Hrgota proving pivotal during the opening period.

Title rivals RB Leipzig went down to a goal from Wolfsburg's former Bayern striker Mario Gomez and, with 10 games remaining this season, a fifth consecutive Bundesliga crown appears an increasing formality for the Bavarian giants.

Frankfurt spurned an unexpected opening in the second minute, with Ante Rebic blazing over after Bayern left-back David Alaba was dispossessed.

It was a lethargic start from the hosts and only a stunning last-ditch tackle from Hummels prevented Hrgota from putting Frankfurt ahead after he rounded Manuel Neuer.

Costa, one of the few bright sparks for Carlo Ancelotti's men during the first half-hour, sliced over from Alaba's cross but Frankfurt continued to operate on the front foot.

It was therefore against the run of play when Lewandowski slotted home his 20th Bundesliga goal of the season in the 38th minute, Thomas Muller sliding a low ball across the face of goal after the Poland striker's flick-on caused confusion in the visitors' defence.

Hrgota's frustrating outing in front of goal continued when he spurned the opportunity to register an instant Frankfurt response, stabbing wide at the back post following fine work from Rebic.

Again, profligacy was punished, with Alaba darting down the left and teeing up Costa for an emphatic finish and a somersault celebration.

Muller thought he had added to his solitary Bundesliga goal this season but Makoto Hasebe made a sliding goal-line clearance, the Frankfurt defender thumping his knee on the base of the post for his troubles.

Niko Kovac's men were not cowed into abandoning their attacking intent and the impressive Rebic cut into the box to hit the crossbar before Danny Blum shot wildly over.

Bayern gave their opponents a lesson in efficiency once more, with Arjen Robben shifting on to his left foot to pick out Lewandowski, whose control and finish was impeccable to reach his landmark.

Hasebe was still feeling the effects of his earlier intervention in the 64th minute and he made way, meaning a first Bundesliga appearance for Marco Russ since the 31-year-old received the all-clear from testicular cancer treatment.

Blum kept Neuer honest, drawing a sharp low save from the Germany goalkeeper, who was protected by Jerome Boateng for the first time this calendar year – the centre-back replacing Javi Martinez midway through the half to mark a return from shoulder surgery.

Lewandowski passed up a chance to claim the matchball, slotting past the post after Robben played him through.

Frankfurt lie sixth despite their losing run in the Bundesliga being extended to five matches and remain in contention for a European place.

Bayern's loftier ambitions are set to be realised sooner rather than later.