The Russian world number 30 claimed seven consecutive games to win the first set in 26 minutes and take a 1-0 lead in the second before Zeballos put up more of a fight.
Youzhny, who reached the final of the Japan Open earlier this month, was finally able to subdue his 54th-ranked opponent by clinching the tiebreak 7-5.
He may be face Potito Starace for a place in the last eight after the Italian eliminated Russian Evgeny Donskoy 6-3 6-3.
Fifth seed Pablo Cuevas of Uruguay also went through with a 6-4 6-2 win over Taiwan's Lu Yen-hsun to set up a second-round encounter with Russian Teimuraz Gabashvili, who overcame Slovak Karol Beck 3-6 6-4 6-4.
In-form Russian Nikolay Davydenko, who won the Shanghai Masters on Sunday to climb to number six in the world, heads the field at the annual indoor tournament in Moscow and will take on compatriot Marat Safin in the first round on Wednesday.
On the women's side, fifth seed Nadia Petrova crushed fellow Russian Yana Buchina 6-2 6-0 to reach the second round where she will face Ukraine's Alona Bondarenko, a 6-4 6-3 winner over Russian Anna Chakvetadze.
However, seventh-seeded Slovak Dominika Cibulkova was upset by Spain's Maria Sanchez Martinez 6-2 6-2.