Bayern enjoyed almost total dominance but were shaken when Thorben Marx converted a harshly-awarded penalty for Gladbach midway through the first half.
Marx went from hero to villain when his misplaced pass fell to Shaqiri, who joined from Basel at the start of the season, and the 21-year-old Kosovo-born Swiss international fired the equaliser in the 59th minute.
"We dictated the game and they hardly had a scoring chance," Bayern coach Jupp Heynckes told reporters.
"[Gladbach keeper Marc-Andre] Ter Stegen was the best player on the pitch. He was outstanding."
Sixth-placed Gladbach survived an early battering and went ahead when Tolga Cigerci's cross hit Jerome Boateng's elbow from close range as the defender turned away and Marx confidently steered the penalty low into the right corner.
Bastian Schweinsteiger's free-kick was headed off the line by Juan Arango with Ter Stegen beaten and Brazilian Dante's header scraped the crossbar in the next attack as Bayern hit back.
Ter Stegen made an outstanding save at full stretch to stop Schweinsteiger's low shot from finding the bottom corner.
Television replays suggested a defender made slight contact and that Gomez's theatrical fall was an exaggeration.
"I had too much to do but we fought hard and worked hard," said Ter Stegen.
