The Germany striker opener the scoring in the fifth minute before completing the rout with a 69th-minute penalty.
Franck Ribery and Bastian Schweinsteiger had made it 3-0 inside the first 13 minutes to lift Bayern five points clear of second-placed Borussia Monchengladbach.
Gladbach conceded three minutes from time as they had to settle for a 2-2 draw at home to Bayer Leverkusen.
Stefan Reinartz gave Leverkusen the lead after 20 minutes before Marco Reus equalised in the 65th minute. Leverkusen went a man down after 68 minutes as Gonzalo Castro was shown the red card.
Patrick Herrmann pushed Gladbach ahead 2-1 after 72 minutes, but Andre Schurrle equalised late on.
Schalke missed the chance to go second as they suffered a shock 2-1 home defeat to Kaiserslautern.
The hosts were up against it after half an hour when goalkeeper Ralf Fahrmann was sent off for a foul on forward Kouemaha and Christian Tiffert put the visitors in front from the spot.
Klaas Jan Huntelaar equalised after an hour from another penalty with Rodnei this time shown red to leave both teams with 10 men, but Kaiserslautern responded and Dorge Kouemaha scored the winner in the 72nd minute.
Stuttgart moved level on points with Borussia Dortmund and Werder Bremen in third with a 2-0 win at home to Hoffenheim.
Shinji Okazaki opened the scoring in the 48th minute and then Pavel Pogrebnyak converted from the spot after 77 minutes to settle the game.
At the other end of the table, Mario Mandzukic scored twice to earn struggling Wolfsburg to a precious 2-1 victory at home to Nuremberg.
The Croatian gave the hosts the lead in the 24th minute only for Christian Eigler to equalise after 70 minutes.
But Mandzukic netted his second from the penalty spot to settle the match seven minutes from time.
Jan-Ingwer Callsen-Bracker's 88th-minute penalty earned Augsburg their first ever Bundesliga victory with a 1-0 win at fellow strugglers Mainz.
The defender held his nerve to give the top flight new boys their first three-point haul at the ninth attempt.
On Friday night, Borussia Dortmund moved up to second in the Bundesliga with a 2-0 victory at Werder Bremen.
Ivan Perisic opened the scoring for the visitors the 43rd minute only to be sent off two minutes into the second half.
But the 10 men sealed the win with a second goal from Patrick Owomoyela in the 73rd minute as Bremen dropped to fourth.
Perisic put the visitors in front two minutes before the interval when he received the ball from Sven Bender, made room for the shot and fired it into the roof of the net.
His joy was shortlived, though, as he saw red two minutes after the break.
Perisic went in hard on Sokratis Papastathopoulos and was shown a second yellow card.
Dortmund were forced to play on the counter attack, and one earned them a corner in the 72nd minute.
Bremen were unable to clear their lines and the ball found its way to Owomoyela, who scored against his former club from close range.