Musiala soared above the defense at the back post to head in an 85th-minute equalizer, halting Dortmund's flawless Bundesliga home record in the 136th clash between the two rivals in Der Klassiker.
Leroy Sane went close for Bayern early on, but it was the home side who opened the scoring with a wonderful effort from Gittens just after the midway point in the first half.
Nico Schlotterbeck played a measured ball to the Englishman on the left touchline just inside his own half, with Gittens stepping over the ball, before racing away from Konrad Laimer and smashing the ball across Manuel Neuer and into the corner.
Harry Kane went off with a suspected hamstring injury minutes later, with the man who replaced him, Thomas Muller, unable to convert with a good chance in each half.
TrendingMusiala and Sane both spurned opportunities in the second half, before Musiala headed in a cross from substitute Michael Olise late on to earn Bayern a share of the spoils
More to follow.