Medvedev, the world number six who is coming off three straight titles at Rotterdam, Doha and Dubai, said his 6-2, 3-6, 6-1 third-round victory over 85th-ranked Ivashka was a "matter of a few points."
"Always tricky to play here," said Medvedev, a former world number one whose best showing in the California desert was the round of 16 in 2021.
"(It's) tough to make anything during the rallies, so just have to kind of see who puts more balls in court. If you lose a little momentum you lose a set."
Medvedev was clearly frustrated at the end of the second set, grumbling to the referee that he would be "as slow as the court" in taking a bathroom break.
He managed to pull himself together, however, to take a 5-0 lead in the third.
Serving to prolong the match, Ivashka went down 0-40, but reeled off three straight points and held serve with an ace to force Medvedev to serve it out.
"I missed less. That's the only thing you can do. You cannot do more," Medvedev said. "It was a matter of a few points.
"Second and third sets for me they were kind of the same, the score is completely different. It's just who plays better the most important points - break points, 30-all. I managed to do better in the third set."
Medvedev lined up a fourth-round meeting with Germany's Alexander Zverev, the former world number two who is seeded 12th as he works his way back from the torn ankle ligaments that ended his 2022 campaign at the French Open.
Zverev said he felt fortunate to come out with a 7-5, 1-6, 7-5 victory over Finland's Emil Ruusuvuori, who Zverev judged "the much better player" in the third set.
