Having gone a goal down at Red Bull Arena following Albert Vallci’s third minute own goal, Die Mozartstadter responded to maintain their imposing start this season.
Ghana international Ashimeru levelled scores in the 33rd minute, before Koita put his team ahead two minutes from that half-time break.
Masaya Okugawa made it 3-1 for Salzburg 10 minutes from restart before the Malian’s second strike of the encounter finished off the Violets.
The duo, alongside Mohamed Camara, were on from start to finish while Patson Daka was introduced in the 80th minute for Maximilian Wober.
For Austria Wien, Bright Edomwonyi replaced Christoph Monschein in the 70th minute while Central African Republic's Sterling Yateke and Guinea-Bissau's Maudo Jarjue were not listed for the game.
Salzburg lead the log with 25 points from nine matches while Austria Wien are in eighth position with eight points.