However, Djokovic, who helped his country beat Kazakhstan in the Davis Cup last week, used his vast experience to overcame the early onslaught and secure a 2-6 6-1 6-2 victory at a breezy Indian Wells venue.
"The fifth game of the third (set) was the deciding one," the Djokovic told reporters.
"That break obviously meant that I can start to feel a bit more comfortable, play a little bit more aggressive on the court.
"It was swirly conditions. Trying to win with experience and with toughness in the clutch moments. That's what helped me to prevail."
Djokovic, 11-times a grand slam singles champion who is bidding for a record fifth title in Indian Wells, will next face Germany's Philipp Kohlschreiber, who dropped only one game in beating American Denis Kudla.
Fourth seed Nadal also had a fight to make the third round in the day's late match, saving 11 of 14 break points to edge out Luxembourg's Gilles Muller 6-2 2-6 6-4.
"I'm very happy for the victory after the last three matches that I lost have been in three sets or five sets. So I needed a victory like this,” said the three-times champion, who will now face his doubles partner Fernando Verdasco.
Women's top seed Serena Williams looked like she was in for a battle but the early challenge of Yulia Putintseva wilted as the American eased to a 7-6(2) 6-0 third round win.
As boxing great Mike Tyson watched on, Williams punched below her weight in the first set, making 29 unforced errors and had to break the Kazak’s service to force a tiebreak.
The second set was not a fair fight as Williams overwhelmed her opponent.
"I started to get more confidence to continue to go for it,” Williams told reporters.
The 34-year-old American ended with seven aces and moved closer to her first title at Indian Wells since her infamous win in 2001, after which she boycotted the event until returning last year.
Serena was booed throughout the 2001 final by a crowd that assigned her the blame for the withdrawal of her sister Venus before their scheduled semi-final.
While Williams got a good workout on Sunday, world number three Agnieszka Radwanska of Poland barely raised a sweat as she continued her bid for a first Indian Wells crown by beating Monica Niculescu 6-2 6-1.
Defending champion Simona Halep breezed past Ekaterina Makarova, while eighth seed Petra Kvitova and last year's runner-up Jelena Jankovic were also winners
In the men's draw, Kei Nishikori cruised past Mikhail Kukushkin 6-3 6-3, while Jo-Wilfried Tsonga and John Isner also advanced but Bulgarian 23rd seed Grigor Dimitrov was dumped out by German teenager Alexander Zverev 6-4 3-6 7-5.
(Writing by Jahmal Corner in Los Angeles; Editing by Andrew Both/Patrick Johnston)
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