Prior to his first-round victory, Djokovic had not played since losing in the Wimbledon semi-finals to Jannik Sinner in early July.
“I’m hoping the deeper I go into the tournament the better I feel about my game,” Djokovic said.
“It’s obviously a little different in the past couple of years for me body-wise.
“I get wear and tear quicker than I ever used to so I have to deal with that, a lot of recovery stuff to try to make myself able to perform at the highest level.”
Playing in the morning session on Arthur Ashe Stadium – an unfamiliar timeslot for a player accustomed to headlining the tournament’s coveted night session – Djokovic seemed out-of-sorts in the bright sunshine.
The seventh seed had looked fatigued in his first-round match and seemed hampered by similar issues early on against home hope Svajda.
The world number 145 went viral before the match after posting a video of his excitement about playing Djokovic but he showed no signs of being overawed, holding his nerve to edge the first set.
But Djokovic, as he so often does, immediately responded, and reeled off 11 of the final 12 games as Svajda struggled with cramp.
Earlier, 21st seed Tomas Machac saw off rising Brazilian star Joao Fonseca in 7-6 (7-4) 6-2 6-3.
The 19-year-old Fonseca, backed by a boisterous fan base on the Grandstand court, had a set point in the opener but Machac held firm to prevail.
His Czech compatriot and 20th seed Jiri Lehecka also progressed with a 3-6 6-0 6-2 6-4 win over Argentina’s Tomas Martin Etcheverry.
