The Bavarians ousted their floundering rivals in style, with David Alaba grabbing two goals in a completely dominant performance from the hosts
Neither side really started the game well. In fact, surprisingly, it was Schalke which had the first sight of goal. Michel Bastos got the ball on the left and took an early shot, but it flew into the side-netting.
Gradually, though, Bayern began to take command. First, Franck Ribery dribbled down to the byline, but rather than crossing, he shot from the narrowest of angles, and had Timo Hildebrand scrambling across his line.
The Konigsblauen defence was standing surprisingly firm, but they should have been a goal behind just after the 15-minute mark, when Schweinsteiger bent in a lovely cross straight onto the head of Robben, who contrived to head wide when he should have scored.
That was as long as the resistance lasted, though. Less than a minute later, Ribery twisted and turned in the box, and was promptly brought down by Marco Hoger. Alaba stepped up to take the penalty, and sent Hildebrand the wrong way.
Scweinsteiger then had a chance to make it 2-0 with another free header, but squandered it. It was not long before he made amends.
Saed Kolasinac took down Robben just outside the box, Schweinsteiger claimed the resulting free kick ahead of the Dutchman and Toni Kroos, and bent it brilliantly into the bottom corner, via the inside of the post.
Bayern started the second half in much the same way it finished the first. Robben drove down to the byline, pulled the ball back, and Gomez was able to touch it into the path of Alaba, who got his second of the game with a neat finish.
Seconds later, it could have been four when Robben and Gomez beat the offside trap, but rather than square it to his teammate, the Dutchman elected to try to chip Hildebrand, and sent the ball onto the roof of the net.
The next time Robben was in a scoring position, though, he did play in the Germany international. Schweinsteiger played a masterful ball over the top to the 29-year-old, who squared it to Gomez, who finally got his goal.
After just a few seconds of stoppage time, the referee blew the whistle. Schalke slips to ninth, but Bayern marches on.