Bayern have already stormed into what may be considered by some an unassailable lead at the top of the Bundesliga but had the chance to increase it further when Augsburg visited on Saturday.
It was the minnows who had the first good chance of the game, however, as the lively Alexis Claude-Maurice struck from distance but couldn't manage to find the target.
Bayern still had most of the ball, boasting over 80% of possession during the first 15 minutes, but Kompany's side failed to do much with it until getting the opener midway through the first half. Michael Olise conjured up his 15th league assist of the season, crossing for Ito to head in from a corner.
The reigning German champions smelled blood in the water and almost got a second goal soon after, but Lennart Karl's streching volley drifted wide after good work from Luis Diaz.
Augsburg kept themselves in the game, not allowing Bayern to overwhelm them, and nearly got an equaliser just before half-time when Robin Fellhauer smashed the bar.
Bayern failed to raise their level in the second half, being too pedestrian in possession, and were made to pay for it when Augsburg grabbed a deserved leveller. Mert Komur's tantalising delivery from a corner was met by Chaves, who buried his header to make it 1-1.
The script was well and truly ripped up when the visitors took a shock lead inside the final ten minutes. Dimitris Giannoulis found space down the left wing and found the free Massengo in the box, the 24-year-old converting calmly from a central position.
Bayern applied some pressure in the final exchanges but couldn't carve out the quality chances needed to get themselves level, with Olise hitting the bar with the final kick of the game, and ended up losing for just the second time in the Bundesliga so far this season.