The Spanish tactician was unable to call on summer signing Thiago Alcantara, who was absent due to illness, but his naming of an attacking lineup soon paid dividends when Bayern raced into a comfortable advantage.
Things got even better for the hosts when Mandzukic pounced to convert from close range on 17 minutes, after Ter Stegen had denied Ribery's initial shot.
The action continued to be one-way traffic, before a mix up between Manuel Neuer and Dante, who headed into his own net at the near post, halved Bayern's lead just prior to the break.
It proved to be only a blip in an impressive performance from Guardiola's outfit, who, after hitting the post through Toni Kroos, were awarded a second-half penalty when Alvaro Dominguez handled inside of the box.
Thomas Mueller's spot kick was well saved by Ter Stegen, but, remarkably, Dominguez was adjudged to have handled again when attempting to clear and Bayern had another chance to make the game safe from 12 yards.
Alaba took over the penalty-taking duties and succeeded where his teammate failed, convincingly smashing the ball into the side netting to secure Bayern victory in their season opener.