Bayern stuff Schalke, Hamburg stun Dortmund
Left-back Alaba scored either side of a sensational Bastian Schweinsteiger free-kick with Mario Gomez, starting ahead of top scorer Mario Mandzukic, drilling in the fourth as Bayern made it four straight wins this year without conceding a goal.
In another impressive display of fluid, attacking football, Bayern outplayed Schalke, launching an avalanche of pressure from the start and missing several other clear chances as they chase their first title after two failed campaigns.
Bayern move on to 54 points with their 17th win in 21 league games while fellow Champions League competitors Schalke, badly missing a string of injured players and having notched only one win in their last 10 games, dropped to ninth.
"In the first 20 minutes it was tough against a hard-working Schalke defence," Bayern coach Jupp Heynckes told reporters.
"After we scored our first goal I knew Schalke would need to come out a bit more and that is where we played really well. It is great fun working with this team at the moment."
Second-placed Dortmund suffered a surprise 4-1 drubbing at the hands of visiting Hamburg SV to remain on 39 points.
Latvian Artjoms Rudnevs and South Korea international Son Heung-min each scored twice and both teams finished with 10 men after Dortmund's Robert Lewandowski and Hamburg's Jeffrey Bruma were shown straight red cards for foul play.
Leverkusen looked to be heading for victory after twice coming from behind to lead 3-2 against Borussia Moenchengladbach but an 86th minute equaliser from Patrick Hermann secured a point for the hosts, leaving Leverkusen in third on 38.
Werder Bremen beat VfB Stuttgart 4-1 with the home side left licking their wounds after a fifth straight defeat that incrases the pressure on coach Bruno Labbadia, who last month extended his deal to 2015.
VfL Wolfsburg climbed further away from the relegation zone with a 1-0 win over bottom side Greuther Fuerth thanks to Bas Dost's eight goal of the season to move up to 12th on 26 points.
Heynckes made three changes to the Bayern side that won the last three league games, bringing in Arjen Robben, forward Mario Gomez for top scorer Mario Mandzukic and defender Jerome Boateng.
It was initially hard work against a crowded Schalke defence and the hosts needed Franck Ribery's explosive skills to set them up for the opener.
Ribery toyed with two defenders in the area before being brought down as he tried to charge past them and Alaba coolly converted the spot kick, sending Timo Hildebrand the wrong way.
It did not take long for the hosts to increase their lead on a freezing Munich evening, with Schweinsteiger smoothly curling a free-kick over the wall and in off the post.
Schalke, missing injured central defender Kyriakos Papadopoulos as well as forwards Klaas-Jan Huntelaar, Ibrahim Afellay and Ciprian Marica among others, could do little to stop the Bayern charge.
Alaba got his se