The third seeded Indo-Pak pair recorded a hard-fought 7-6(5) 6-7(2) 10-3 win over the unseeded Dutch-Romanian team in one hour and 41 minutes.
They next face Treat Huey from Philippines and Briton Dominic Inglot, who ousted Spaniards Pablo Andujar and David Marrero 6-4 6-3 in their opening round of the USD 511,825 hard court event.
Bopanna and Qureshi had suffered a first round exit at last week's Chennai Open in their first match of the season.
India's Somdev Devvarman had failed to qualify for the singles main draw after losing in the second round of the qualifiers.