Die Roten were thankful to their Polish sharpshooter as he came up with two goals, while Arjen Robben also hit the net to ease the pressure on Carlo Ancelotti.
Robert Lewandowski inspired Bayern Munich with a well-taken double as the champions came from behind to beat Mainz 3-1 away from home in the Bundesliga on Friday.
The Poland international was in lethal form as he spearheaded the Bayern attack, while Arjen Robben co-starred with a goal and an assist of his own in his 150th Bundesliga appearance, helping Carlo Ancelotti's men put the pressure back on RB Leipzig at the summit.
Bayern looked to be in a spot of bother early on, though, as Jhon Cordoba – the scorer of a late winner in Munich in March – produced a clinical finish with just four minutes gone.
But the away side did not need long to turn the score on its head, as Lewandowski equalised shortly after and Robben – the architect of the striker's leveller – put the visitors ahead in the 21st minute.
Goalscoring opportunities were generally more scarce from thereon in, with Thomas Muller – passing the 15-hour mark without a Bundesliga goal – continuing to toil without reward.
But Bayern eventually wrapped things up in second-half stoppage time thanks to Lewandowski's precise free-kick, moving them level on 30 points with Leipzig, who host in-form Schalke on Saturday.
Cordoba underlined the high-tempo start to proceedings when he spun away from Mats Hummels and beat Manuel Neuer from a tight angle after racing on to Yunus Malli's throughball.
Bayern hit back swiftly, though, as Robben ran at the Mainz defence and fed Lewandowski into the area for an easy finish.
The visitors began to exert control after equalising and it came as little surprise when they took the lead.
Muller supplied a brilliant cross from the right flank and, although Lewandowski was not quite able to reach it, the ball came down nicely for Robben to meet it with a diving header.
Bayern remained the dominant force for the remainder of the first half, but chances at either end were infrequent as the match became bogged down in midfield.
The visitors continued to see more of the ball after the break, but Mainz's insistence on sitting back in numbers prevented Ancelotti's charges from breaking through.
Bayern eventually carved open an opportunity just after the hour mark, but Robben's first touch proved heavy when through on goal and goalkeeper Jonas Lossl rushed out to tackle him.
Mainz became more purposeful in attack as the full-time whistle approached, but in the end Bayern dealt the hammer blow.
Lewandowski stepped up to a free-kick on the edge of the area and coolly carresed it into the top-left corner, leaving Lossl with no chance.
