The left-handed Indian capitalised on early breaks and saved all six break points he faced in the opening round of the hard court event.
Jeevan, who came into the event after his best finish at Challenger level, next faces American Thomas Shubert.
Later in the day, Jeevan combined with Taipei's Jui-Chen Hung to storm into the doubles quarterfinals.
The second-seeded Indo-Taipei pair trounced local wild card pair of Joshua Cepeda and Brian Tuncap Jr 6-0 6-0.
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