Bonfim Dante opened the scoring with a glancing header that nestled in the bottom corner.
Shaqiri scored when he got a lucky ricochet then saw his shot deflect over Freiburg goalkeeper Oliver Baumann, before the Swiss doubled his tally for the afternoon, finishing off a slick Bayern counter.
Freiburg were left feeling aggrieved that a legitimate goal was incorrectly chalked off for offside on the stroke of half time, before Claudio Pizarro wrapped up the win late in the game.
Bayern coach Pep Guardiola demonstrated the versatility of his squad by leaving five players that featured in the 5-0 thrashing of Hamburg in the DFB-Pokal clash in midweek on the bench.
Thiago Alcantara, Jerome Boateng, Mario Gӧtze, David Alaba and Mario Mandzukic all started this one in the dugout as many of Bayern’s peripheral players staked their claim for a regular starting berth, with the Champions League clash against Arsenal on the horizon.
It was one of the regulars that notched up the game’s first goal, however, with Dante scoring with the game’s first real chance. Philipp Lahm rolled the ball out to Diego Contento, whose pacey cross was glanced into the bottom corner by the big Brazilian.
Bayern started to boss the contest and doubled their lead through Shaqiri. The Swiss got a lucky ricochet and, after realising where the ball was, then had another slice of luck, with his shot deflecting off Oliver Sorg and beyond the helpless Oliver Baumann in the Freiburg goal.
Bayern effectively put the game to bed with another from Shaqiri after a blistering Bayern counter-attack. Toni Kroos drove forward and cut back for Shaqiri, whose goalbound shot took a slight deflection off Thomas Muller on its way in.
In a rare foray forward, Freiburg were denied a legitimate goal on the stroke of half time, with Admir Mehmedi incorrectly flagged offside as he prodded in from close range.
Freiburg improved in the second half and their best chance fell to substitute Sebastian Kerk, who was sent clean through but dragged his shot narrowly wide of Manuel Neuer’s far post.
With the game won in the first half, Bayern took their foot off the pedal in the second, with easy chances for Contento and, in the closing stages, Javi Martinez, going begging – but they got a fourth late on when Pizarro cut into the box and guided a low shot into the far corner.
Later, Klaas Huntelaar headed home in the 74th minute to spur Schalke 04 to a 2-1 victory over second-placed Bayer Leverkusen ensuring the 16 point gap remained.
The Netherlands striker had his back to the goal but outleapt his marker to score a glancing header off a 40-metre Jefferson Farfan free kick just five minutes after Leverkusen had equalised with a Felipe Santana own goal.
"I always had the feeling we'd get our chance and when we did we took advantage of it," said Huntelaar. "It tastes good to get the three points here at Leverkusen."
Schalke, in fourth place with 40 points, had deservedly taken a 1-0 lead in the 33rd minute when Leon Goretzka took advantage of a Leverkusen blunder. Schalke host Real Madrid in the Champions League on Wednesday.
Third-placed Borussia Dortmund, with 42 points, downed Eintracht Frankfurt 4-0.
Hamburg SV's woes continued with an eighth successive defeat, 4-2 to Braunschweig.
Hamburg, the only Bundesliga club never to be relegated, fell deeper into the relegation zone in a blunder-filled performance against last-placed Braunschweig, raising further speculation that coach Bert van Marwijk would be sacked.
Germany goalkeeper Rene Adler had an especially dreadful afternoon, with two second-half errors that led to goals. Domi Kumbela came off the bench to score three second half goals for Braunschweig
Last week Hamburg looked at hiring Felix Magath as their coach. Magath was interested but could not reach an agreement with HSV management. On Friday Premier League bottom club Fulham appointed Magath as their manager on an 18-month contract.
Van Marwijk said his side had made unnecessary defensive mistakes. "If you give away goals like that it's hard to do anything."
He brushed aside suggestions that he would be sacked. HSV said the club would review the situation on Saturday night.
"The best medicine would be to win a match or two to regain some confidence," said van Marwijk I'm doing everything I possibly can to help HSV."