The second-seeded Tsitsipas had his shoulder taped and the injury appeared to affect his backhand.
Jordan took advantage and attacked the Greek´s backhand while charging in on short balls to earn his second career win over a top-10 player.
He finished off Tsitsipas, the Australian Open runner-up, in two hours, 37 minutes.
Before the game Tsitsipas had mentioned.
"I am still recovering [from right shoulder injury] and I won't pretend that I have a chance to do well in these next two tournaments. I don't think I'll be capable of going deep. The priority is to prepare my body for the clay court swing".