Traore gave Stuttgart an early lead before Koo Ja-cheol equalised for Augsburg on the stroke of half-time with an excellent individual effort.
Ibisevic scored Stuttgart's decisive second in the 69th minute as the hosts won for the second time in three games to improve to 19 points.
Augsburg's winless streak now stands at seven matches and they remain on seven points.
Stuttgart went in front on 11 minutes as Ibisevic raced down the right side and crossed into the box where Traore fired home from five yards.
Both teams ventured forward time and again in an open first half and the visitors deservedly pulled level in the 44th minute thanks to a fine solo effort by Koo, who collected the ball in the midfield, raced on and pirouetted away from his marker before unleashing a fearsome 25-yard strike into the top-left corner.
The hosts were close to regaining the lead three minutes after the break but Traore headed just wide.
Traore nevertheless had a hand in restoring Stuttgart's lead in the 69th minute as the Guinea international's free-kick from the right was met with a strong header by Ibisevic which flew in at the near post.
Augsburg did not give up and Stuttgart goalkeeper Sven Ulreich had to parry a powerful strike by Daniel Baier.
Koo came close to levelling moments later but his initial effort was saved by Ulreich before the South Korean lashed the rebound wide of the target.