Second seed Youzhny lost to little-known German Michael Berrer 7-5 6-4, while the third-seeded Scot succumbed to Serb Janko Tipsarevic 6-4 7-5.
In the women's draw, last year's winner and third seed Anna Chakvetadze was beaten by fellow Russian Dinara Safina 7-6 6-2 to join a growing list of high-profile players, including Maria Sharapova and Amelie Mauresmo, who have bowed out of the $2.3 million (1.1 million pound) indoor tournament.
Men's top seed and defending champion Nikolay Davydenko did advance, overcoming Nicolas Lapentti of Ecuador 6-4 6-4.
In Friday's quarter-finals, he will face 2004 winner Igor Andreev, who beat another member of the Russian Davis Cup team Marat Safin by the same score.
It was a frustrating afternoon for Murray, making his first appearance in Moscow, as the world number 18 argued in vain with the umpire about a number of disputed calls in the second set.
"I didn't feel like I played too badly. I played one bad game to lose my serve in the first set, but in the second I had so many chances," he told reporters.
"I was 5-2 at 15-40 on his serve, then I lost my serve, I also had 0-40 on his serve at 5-4, but I had some pretty rough calls go against me. It was tough as I felt like I should have been in the third set."
Murray's match was played on court one which was not equipped with the Hawk-Eye electronic system, allowing the players to challenge a call.
The 20-year-old said he was not feeling tired after reaching the final at last week's Metz Open.
"No, I wasn't that tired, I'm still upset because I feel like I deserved to win that second set."
SLEEPY SERENA
In the first match on centre court, former world number one Serena Williams had to work harder than expected to see off Ukrainian qualifier Tatiana Perebiynis 7-5 6-4 and move into the quarter-finals.
"I don't think I've played up to my standards today but I was glad to be through," said the fourth-seeded American, who is making her second appearance in Moscow, 10 years after her debut.
"I was working on some things...It might not work in this match but in the future it's gonna work well for me."
The Australian Open champion, who was playing her first match after receiving a bye into the second round, said it was hard for her to get up for such an early start.
"Actually I like playing indoors on such a (fast) surface, it suits my game but I needed two cups of coffee to wake up," she said. "Usually I'm still sleeping at this time (11 a.m.), so it took me a while to get going."
Williams will now meet eighth-seeded Czech Nicole Vaidisova, who eased past Russian wildcard Elena Vesnina 6-3 6-4.
Unseeded Russian Vera Zvonareva, who knocked out former world number one Mauresmo in the first round on Wednesday, continued her good vein of form with a 6-2 6-2 victory over talented teenager Agnieszka Radwanska.
The 18-year-old Pole, who stunned Sharapova in the third round of the U.S. Open last month to rise to number 33 in the world, had no answer to Zvonareva's power game and bowed out in 72 minutes.
