The fourth seed from Norway struggled to keep things under control in the match against claycourt specialist Jarry, who led in the last two sets but could not convert.
Ruud next faces either Dane Holger Rune, in a rematch of last year's quarter-final, or Argentina's Francisco Cerundolo.
"If we had gone five sets I don't know how long we would have played," said Ruud on Court Philippe Chatrier.
"I have to thank my team for pushing me in practice. I did the work and physically I was ready for more."
Ruud wasted a break advantage and was pushed into a tiebreak, which he won comfortably.
Possibly lulled into a false sense of safety, Ruud fell a 4-1 behind in the second set but he rallied back and won six of the remaining seven games to edge closer to victory.
The lanky Chilean, taking part in his first last-16 singles match at a Grand Slam, did not give up and again took the first break in the third set.
With his big shots, Jarry was always in the contest and if the match had been played on a smaller court, the outcome might have been different as no player would have wanted to be Ruud against such a huge first serve.
"It is probably the biggest clay court in the world, so it made the returns easier and safer," said Ruud.
