The Polish striker was left unmarked at the far post to tap the ball in after Gladbach had come from a goal down to lead 2-1.
The result left both teams on 10 points with Gladbach in fifth place and Augsburg sixth.
Augsburg took a 27th-minute lead when Andre Hahn drilled the ball in from a tight angle after Juan Arango had rattled the bar for the visitors.
Gladbach levelled six minutes later through forward Max Kruse who struck his fourth league goal of the season to boost his chances of a Germany call-up for next month's World Cup qualifiers with Mario Gomez and Miroslav Klose injured.
Augsburg were again the livelier side after the break and Halil Altintop came close with a header in the 64th minute following a Hahn cross.
Gladbach went in front against the run of play when a Kruse cut-back was excellently converted by substitute Branimir Hrgota after 71 minutes.
Three Gladbach defenders were then caught napping in the 88th minute, allowing Hahn's low cross to float beyond the goalmouth to Milik at the far post.
On Saturday, leaders Borussia Dortmund entertain Freiburg, who have yet to win this season, while second-placed Bayern Munich host VfL Wolfsburg.