Alaba opened the scoring from the penalty spot in the 19th minute and then made it 3-0 at the start of the second half after Bastian Schweinsteiger had doubled Bayern's lead with a free-kick.
Mario Gomez completed the rout in the 63rd minute as Bayern took full advantage of second-placed Borussia Dortmund's surprising home defeat to Hamburg and third-placed Bayer Leverkusen draw at Borussia Monchengladbach to further strengthen their grip on top spot.
Schalke, meanwhile, remain stuck in mid-table after recording just one victory in their last 11 league matches.
Bayern nearly went ahead after 11 minutes but Schalke keeper Timo Hildebrand made a fine save to keep out Franck Ribery's effort.
Munich took the lead eight minutes later from the spot as Alaba converted into the bottom left corner after Marco Hoger felled Ribery in the box.
Schweinsteiger doubled the lead after 32 minutes with a superb curling free-kick over the wall and in off the near left post.
Schalke, who started with just one striker in Teemu Pukki, could muster no real threat going forward and Bayern increased their lead six minutes after the restart as Alaba fired home left-footed following a pass from Gomez.
Arjen Robben missed a chance to make it 4-0 on the counter-attack, looping his shot onto the roof of the net in the 55th minute, but the Dutchman was involved as the home side did add a fourth just after the hour.
He collected a pass from Schweinsteiger before playing it into to Gomez, who made no mistake with his finish.
Gomez thought he added a second goal in the 79th minute but was ruled offside.