The sixth seed was severely tested by the Romanian qualifier, who responded excellently to going a set down to force a decider, only for the Spaniard to win every game in the final set to progress in two hours and 20 minutes with a 6-4 3-6 6-0 win.
However, Granollers will not be joined in the second round in India by compatriot Albert Ramos, who slipped to a 6-1 6-3 loss to Edouard Roger-Vasselin.
Roger-Vasselin, seeded seventh for the ATP 250 hard-court event, broke Ramos' serve three times in the first set, before easing through in the second to seal victory.
And there was to be another Spanish casualty in the day's only real shock, eighth seed Roberto Bautista Agut falling to Russian qualifier Alexander Kudryavtsev 6-4 3-6 6-3.
Bautista Agut bounced back after surprisingly dropping the first set, but his fightback attempt fell short as world number 270 Kudryavtsev emerged triumphant.
Benjamin Becker was the victor in the all-German clash as his countryman Julian Reister retired in the second set with Becker ahead 6-4 2-1.
Spain's Guillermo Garcia-Lopez cruised through with a 7-5 6-0 win over Kazakhstan's Aleksandr Nedovyesov, and Slovenia's Aljaz Bedene beat Swiss qualifier Henri Laaksonen 6-3 5-7 7-6 (7-0) in two hours and 29 minutes.
Home success came in the form of wildcard Yuki Bhambri, who overcame Spaniard Pablo Carreno Busta 6-4 6-3, while Ramkumar Ramanathan, making his ATP World Tour debut, won the all-Indian clash against 2009 finalist Somdev Devvarman 4-6 6-3 6-4.