Djokovic, 30, found little resistance from Granollers, grabbing two breaks early on in the first set and powering to a 6-3 6-4 6-2 victory.
It was a similar story early in the second set with the Serbian world No.2 returning everything Granollers tried to throw at him as he went 4-1 up before a wobble saw him fail to convert eight set points at 5-3.
Dkokovic kept his cool to earn the second set and pounced on the Spaniards' accumulating mistakes in the third set to seal victory on his first match point.
Fifth-seed Milos Raonic of Canada has made light work of 38th-ranked Steve Darcis to cruise into the next round.
Raonic took just 92 minutes to beat Belgian Darcis 6-3 6-4 6-2 - taking the final game to love.
There was better news for Darcis's compatriot David Goffin, with the 10th-seed way too good for local veteran Paul-Henri Mathieu 6-2 6-2 6-2.
Croatian Marin Cilic, the seventh-seed, beat Latvia's Ernests Gulbis 6-3 6-3 6-3.
Ninth-seed Alexander Zverev's first-round match against Spain's Fernando Verdasco was suspended due to rain and poor light.
Germany's Zverev lost the first set but battled back to win the second before play was called off for the day with the score at 4-6 6-3.
Frenchman Richard Gasquet, seeded 24th, beat Belgium's Arthur De Greef 6-2 3-6 6-1 6-3.
After some four-and-a-half hours, including a final set that lasted 96 minutes, veteran David Ferrer rallied past Donald Young.
Ferrer, seeded 30, took his first-round record at Roland Garros to 15-0 with a 5-7 6-3 4-6 6-3 13-11 victory.
Uruguay's 22nd-seed Pablo Cuevas has brushed aside Maxime Hamou 6-3 6-2 6-4.
American 25th-seed Steve Johnson was pushed all the way by Yuichi Sugita of Japan before he prevailed 6-3 6-3 6-7(4-7) 6-7 (3-7) 6-3.
Jack Sock was the biggest casualty in the men's draw to date, the 14th-seeded American eliminated by Czech Jiri Vesely 7-5 7-5 6-3.
Frenchman Gilles Simon was another seed to go out after a 1-6 6-2 6-4 6-1 defeat to Nikoloz Basilashvili of Georgia, while 32-seed Mischa Zverev of Germany crahed out at the hands of Italy's Stefano Napolitano 4-6 7-5 6-2 6-2.
Spanish veteran Feliciano Lopez has defeated Bjorn Fratangelo 6-4 7-6 (7-4) 6-3, while Croatian 20-year-old Borna Coric saw off Mathias Bourgue 7-6 (7-5) 6-3 6-2.
Other first-round winners were Fabio Fognini, Andreas Seppi, Joao Sousa, Viktor Troicki, Simone Bolelli, Diego Schwartzman, Nicolas Kicker, Aljaz Bedene, Rogerio Dutra Silva, Konstantin Kravchu, Victor Estrella and Sergiy Stakhovsky.