Youzhny, the 2004 winner, beat Andrey Golubev of Kazakhstan 6-3, 6-2, while Safin, who won consecutive titles in 2000-01, ousted Richard Gasquet of France 7-6 (5), 6-4.
Youzhny, fresh from winning the Kremlin Cup last week for his fifth career title, broke 139th-ranked Golubev early in the first set and jumped to a 4-0 lead in the second.
"Then there was no trouble to bring it to the victory," said a relieved Youzhny, who admitted to feeling tired.
Two-time Grand Slam champion Safin is playing in his last season on the ATP Tour. The Russian fired 14 aces and closed the match on his second match point when Gasquet returned wide and long.
In second-round action, second-seeded Victor Hanescu of Romania beat Illya Marchenko of Ukraine 6-3, 6-4. Hanescu, a semifinalist last year, reached his first quarterfinal in 11 events since July.
Ernests Gulbis of Latvia upset fourth-seeded Jeremy Chardy of France 7-6 (7), 6-3 to secure a spot at the Australian Open.
"I won 28 points on my first serve in the first set. He played well and I was lucky to win several key points on the tiebreaker," said Gulbis, who won five consecutive games in the second set.
Eighth-seeded Horacio Zeballos of Argentina also progressed, ousting Ukrainian qualifier Oleksandr Dolgopolov Jr. 6-3, 6-4.
Karol Beck of Slovakia retired because of flu while trailing Bjorn Phau of Germany 6-4, 2-1.
Also, Russia's Igor Kunitsyn upset seventh-seeded Pablo Cuevas of Uruguay 6-4, 6-3 in the first round.