With both men having lost their opening match in their first red group encounters, the two headed into their Thursday (AEDT) match knowing they needed a victory to stay in the semi-final hunt.
Now, it will be 2019 Finals winner Tsitsipas who remains in the mix after seeing off 2020 champion and former US Open winner Medvedev across a two-hour-and-21-minute encounter, handing Novak Djokovic the group in the process.
The Greek second seed looked to be racing away to an early finish after cruising to the first set, but found himself embroiled in a much closer follow-up.
A bruising second set forced the pair into a lengthy tie-break, which stretched its points out to double figures before Medvedev prevailed.
The two could then not be separated in the third, only for Tsitsipas to dominate the tie-break the second time around and race away to a crucial win that sets up a winner-takes-all clash with Andrey Rublev.