Bayern effectively German champions
The win took treble-chasing Bayern three points clear of Schalke with a one game left and a 17-goal difference over their rivals, making it all but impossible for them to be caught.
Louis van Gaal's team have also reached the final of the German Cup, where they face Werder Bremen, and the Champions League, where they play Inter Milan.
The Dutchman, who was in danger of losing his job after a poor start to the season, has already won league titles with three clubs in two countries and Bayern will clinch their 22nd German title after last winning in 2007/08.
The formality of completing the first part of the treble will be complete when Bayern visit Hertha Berlin next Saturday.
Twenty-year-old Muller, who has been drafted into the team by Van Gaal this season, struck twice in a devastating start by Bayern against a demoralised Bochum team who fired coach Heiko Herrlich only 48 hours before the kickoff.
"The first 25 minutes was the best football we have seen here in the Allianz Arena this season," Van Gaal told reporters. "They were unbelievably beautiful goals.
"I expected that Schalke were not going to win today, it's a very beautiful day."
"We're going to celebrate. I'm a celebration beast," said Van Gaal, whose players knelt in front of the South Curve hardcore fans as they celebrated at the end.
Schalke 04 coach Felix Magath had predicted that Bayern would falter but was made to regret his words as Mesut Ozil and Hugo Almeida scored second-half goals in Gelsenkirchen to leave his team contemplating their fourth second-place finish since 2001.
Ozil's was a superb effort as he weaved his way past several defenders before placing his shot in the corner.
Defeat by Bayern sent Bochum into the drop zone with 28 points from 33 games, behind Nuremberg - who lost 4-0 at Hamburg SV and occupy the relegation play-off place - on goal difference.
Hanover 96 leapfrogged both teams to 15th with an astonishing 6-1 demolition of Borussia Moenchengladbach.
Bottom club Hertha Berlin were relegated after a 1-1 draw at Bayer Leverkusen left them four points adrift.
Ivica Olic, scorer of a hat-trick in the 3-0 win at Olympique Lyon which sent the Germans to the Champions League final on Tuesday, missed a couple of early chances as Bayern took control.
The Croatia forward shot wide with only goalkeeper Philipp Heerwagen to beat and failed to make contact when Franck Ribery's low cross flew across the face of the goal.
But the goal was only a matter of time and Muller provided it by chesting the ball over the line after Philipp Lahm's low cross beat Heerwagen.
Two minutes later, Muller headed the second after Ribery sidefooted Lahm's high cross back across the face of the goal.
Muller was denied a hat-trick when his shot hit the post early in the second half from Ribery's incisive pass.
But he was not to be denied and, in the 69th minute, collected an Mark van Bommel pass, sidestepped a challenge and slotted the ball past Heerwagen.
Dariusz Wosz took charge of relegation-threatened Bochum, becoming the team's fourth coach, including interims, of the season.