Augsburg have now lost six of their last seven Bundesliga games and sit precariously above the relegation zone, but did pull a goal back from the penalty spot through Daniel Caligiuri.
Visiting goalkeeper Rafal Gikiewicz saved Olmo's initial effort. However, the Video Assistant Referee (VAR) ordered a retake after the keeper stepped off his line.
Olmo scored from his second attempt, bravely picking out the same corner but this time packing too much power for Gikiewicz.
It was 2-0 before half-time after Yussuf Poulsen broke behind the visiting defence and his cross provided a tap-in for former Paris Saint-Germain forward Nkunku.
It was one of just two shots on target for them in a game that was not nearly as close as the scoreline suggested.