The Austria international struck early in the second half to secure three points for the Bavarians, who have gone eight points clear ahead of Dortmund.
Bayern Munich took another step towards retaining their Bundesliga title thanks to a hard fought 3-1 victory away to Stuttgart on Saturday.
A Georg Niedermeier own goal on the half-hour mark and David Alaba's smartly taken first league goal of the season shortly after the interval looked to have given Bayern a comfortable win, before a remarkable piece of improvisation from Daniel Didavi threatened to make a game of it for Stuttgart.
A Douglas Costa strike sealed the victory late on, and moved Bayern eight points clear of second-placed Borussia Dortmund, who play Schalke on Sunday.
Bayern were gifted the lead when Stuttgart captain Niedermeier deflected a low Franck Ribery cross from the left into his own net. Niedermeier was at full stretch in a vain attempt to prevent an easy tap-in for the waiting Robert Lewandowski, but he could not keep the ball from squirming past Przemyslaw Tyton in the Stuttgart goal.
Alaba stretched Bayern's lead five minutes into the second period, the 23-year-old Austrian's neat footwork controlling and then shifting the ball past a static Stuttgart defender in a crowded penalty area before poking past Tyton at his near post.
Stuttgart's top goalscorer Didavi threatened to make a game of it ten minutes later, somehow hooking the ball above and over Manuel Neuer while lying flat on his back. Bayern's backline had failed to clear a deep free-kick into their area, and the ball ricocheted to the prone midfielder to grab his 11th of the campaign.
Stuttgart pressed for the equaliser, leaving themselves exposed at the back, allowing substitute Costa to collect the ball 25 yards from goal and drive into the bottom left hand corner of Tyton's net.
The victory stretched Bayern's remarkable winning streak over Stuttgart to 15 games, the home side's last victory over the reigning Bundesliga champions coming all the way back in March 2010.
Pep Guardiola used his side's five-point cushion at the top of the Bundesliga as an opportunity to rest key players ahead of their Champions League quarter-final second leg with Benfica, skipper Philipp Lahm, Thiago Alcantara, Douglas Costa and Thomas Muller all dropping to the bench.
But Muller was called into action earlier than expected, replacing Arturo Vidal after just 27 minutes, with Guardiola opting to withdraw a player at real risk of not making it to half-time and lucky to still be on the pitch after pair of reckless challenges just moments apart midway through the half.
Niedermeier's calamitous intervention was a fortunate breakthrough for Bayern, who, having won their last three games 1-0, again struggled for fluency in the first half.
It was Stuttgart who had enjoyed the best opportunity of the first period before the goal, but Didavi was denied by a wonderful point-blank save from Neuer, the midfielder having emerged unmarked at the far post from a free-kick from the left.
Alaba's smart finish, the versatile star somehow creating space to bring the ball down and fire home in a crowded penalty area, looked to have secured a comfortable win for the visitors, but Didavi's brilliance made it a nail-biting finish. Costa, who had earlier hit the bar with a curled effort, extinguished any hopes of a late equaliser for his third league goal of the season.
