The twice Roland Garros champion breezed through the first two sets before encountering resistance from the American whose lack of experience then showed in the tiebreak on the world's biggest clay court.
Djokovic ended the contest with a sizzling service return on his first match point and will face Hungarian journeyman Marton Fucsovics for a place in the third round.
"It's always a pleasure to come back here, one of the best tournaments in the world," said Djokovic, who made his Roland Garros debut in 2005.
"I'm very motivated to go far here, all the way I hope."
Djokovic did not have an ideal build-up to the claycourt Grand Slam, missing the Madrid Masters and being eliminated in the last eight in Rome, but he looked in good form in wind conditions.
On court Suzanne Lenglen, Benoit Paire kept his cool but could not avoid yet another defeat in the main Tour when he was beaten in five sets by British 14th seed Cameron Norrie.
Paire, given a wildcard, was up a break in the decider but could not close out the match.
"I'm happy with all the efforts that I've been making for some time. So today it was a great match," said world number 149 Paire, who has not won in the main draw in a top tier event since August.
