Jonathan scored a hat-trick in Salzburg's opening group win over Elfsborg and another strike from the Spaniard, plus a late second from Andre Ramalho Silva, helped settle a match that produced three red cards on Thursday night.
Both teams had players dismissed in separate incidents just before half-time, Standard midfielder Mehdi Carcela-Gonzalez and Salzburg forward Sadio Mane both picking up two yellows, before the visitors were reduced to nine men when Antonio Kanu was sent off in the 67th minute.
Standard did pull a goal back through Geoffrey Mujangi Bia's 88th-minute penalty, but the damage had already been done.
The result leaves Salzburg top of the group with their 100 per cent record while Standard, who have lost their way in recent weeks after winning their opening nine league games, remain on one point.
Salzburg had the better of the few chances on offer in the opening half-hour but Ramalho's far-post header was blocked by Kanu while he and Sadio Mane failed to trouble visiting keeper Eiji Kawashima with other efforts.
Salzburg keeper Peter Gulacsi was also having a quiet first half and he was able to watch Carcela-Gonzalez's 36th-minute effort fly wide in a rare Standard effort on goal.
That proved to be Carcela-Gonzalez's last positive contribution for his side as two minutes later he was shown a second yellow card for a foul on Mane.
However, his dismissal was not the boost Salzburg would have hoped for as within four minutes they too were down to 10 men as Mane, having been booked early on, was also sent off after picking up a second caution.
Salzburg again started the stronger after the break but once more failed to hit the target with shots from Jonathan, Christoph Leitgeb and Kevin Kampl.
However, that was all to change in the 53rd minute as Jonathan opened the scoring, the former Barcelona B forward slotting home left-footed into the far corner after a blocked shot had fallen kindly for him.
The Austrian side then found themselves in an even stronger position 15 minutes later when Kanu was shown a straight red card for violent conduct, and when Ramalho made it 2-0 with a close-range finish in the 85th minute the game looked over.
Standard gave themselves a glimmer of hope when Mujangi Bia slotted home from the spot after Michy Batshuayi had been fouled by Martin Hinteregger, but Salzburg held on for the points.