The fourth seed was on the back foot for large portions of what wasn't the highest-quality contest, and even trailed 4-1 in the final set against the German, who possesses a punishing single-handed backhand.
However, Auger-Aliassime discovered a second wind towards the end of the fifth, finding the crucial break to get back on level terms before eventually staggering over the line in a 10-point tiebreak.
The Canadian's backhand was under major pressure throughout the match and often broke down, with 68 unforced errors illustrating that. But with nine aces and 54 winners, he was able to rely on his serve and forehand in the big moments.
Auger-Aliassime has already performed better in Paris in comparison to last year, after falling to Matteo Arnaldi in the first round in 2025.
He will face Argentina's Roman Andres Burruchaga next, and following Medvedev's elimination earlier today from this section of the draw, Auger-Aliassime will be hoping to take advantage.