Tevez is reportedly the world's highest paid player on around $1,000,000 per-week, while the Roar players and staff were having issues receiving payment as recently as August 2016.
Yet none of that seemed to matter in the opening two minutes when Brisbane took a shock 1-0 lead.
Tommy Oar broke down the left-wing and delivered an inch-perfect cross to Brandon Borrello who smashed the ball home with a powerful volley.
Borrello, 21, nearly made it 2-0 in the 11th minute as his curling effort from distance rattled off the far post.
Shanghai, looking sluggish, still posed a threat through the individual brilliance of Tevez, Martins and Colombian international Giovanni Moreno, but Roar's collective defending stopped them at every turn.
The second goal was nearly as shocking as the first. This time Borrello was provider, producing a calm cut-back for Oar who smashed home with his little-used right foot.
It was a more nervy affair in the second half as Shanghai pushed forward, but Brisbane continued to threaten on the counter-attack. Oar produced a fantastic solo run that bamboozled four defenders but his shot was well saved.
At the other end, Roar 'keeper Jamie Young produced an incredible reflex save to flick Martins' shot onto the post an away from danger.
It was a performance that will be remember for years by Roar fans, Brisbane knocking out the multi-millionares of Shanghai to move onto the AFC Champions League group stage.