Kovac’s men were on course to maintain their perfect start, looking comfortable heading into the closing stages following Arjen Robben’s strike early in the second half.
However, after failing to beat Augsburg goalkeeper Andreas Luthe again and seeing a late effort from substitute Franck Ribery ruled out for a marginal offside against Thomas Muller in the build up, Augsburg produced a shock equaliser.
With just four minutes left, defender Felix Gotze – returning to face his former club following a summer transfer – knocked the ball in from close range after Manuel Neuer dropped a routine catch from a corner.
While Bayern remain top of the table, the advantage is now down to just two points after Werder Bremen earlier maintained their own unbeaten start with a 3-1 home win over third-placed Hertha Berlin – who await Kovac’s side on Friday night.
“When you’re 1-0 up in the Bundesliga it’s always dangerous,” the Bayern coach said at a press conference.
“Augsburg did a very, very good job over 90 minutes. They stifled our build-up play. It wasn’t easy to get out of our own half. When we did we failed to convert our chances into goals.
“We would have liked to take the three points, but unfortunately failed. We will try to do better away to Berlin.”
Augsburg had made the short trip to the Allianz Arena more in hope than genuine expectation of a shock result following successive defeats.
Coach Manuel Baum said: “We are very happy we have taken a point at the Allianz Arena. You need a passionate and committed team display and luck to achieve it, and we had both.”