Draper said he was “really proud” to make a winning return to the tour following “a lot of down moments [during] the last eight months”.
Seeking to build on the victory over the 68th-ranked Halys, Draper made an assured start on serve as he lost just two points across his opening four games.
But he crucially failed to take his first two break points in the 11th game, before Rinderknech seized his opportunity to clinch the opening set in the following game.
Draper was the first to come under pressure in the second set as he withstood three break points to restore parity at 3-3 but, from the brink of trailing by a set and a break, he reset impressively.
The Briton lost just one point over his next three service games and would not relinquish control of the tie-break after winning four of the first five points.
However, it was Rinderknech who forced the breakthrough in the deciding set – with that proving enough to secure a quarter-final meeting with Russian fifth seed Andrey Rublev.