While a 6-1 7-6 (7-3) 6-2 scoreline may appear routine, Djokovic looked anything but comfortable in the closing stages of a second set that lasted 82 minutes.
The 38-year-old, his black shirt plastered to him with sweat, saved a set point, and a series of gruelling rallies in the tiebreak left him gasping for air.
Djokovic also took a medical timeout at the end of the set for treatment to blisters on his foot, but ultimately used his experience to set up a second-round clash with another American, Zachary Svajda.
"I started great," said the seventh seed. "Just over 20 minutes, first set, I felt really good.
"Then some long games to start the second set, and then I started to feel really (bad) - I don't know why. I really was surprised how bad I was feeling in the second physically.
"We had long exchanges, but also I dropped my level and made a lot of unforced errors and got him back into the match. I'm glad that I kind of reset myself after the second set. And the third set was OK to finish up the match.
"Good thing, two days off now. But it's slightly a concern. I don't have any injury or anything. I just struggled a lot to stay in long exchanges and recover after points.""
Djokovic was playing his first match since losing to Jannik Sinner in the semi-finals of Wimbledon and initially looked sharp against an opponent nearly 20 years his junior.
Tien, 19, announced his talent to the world at the Australian Open in January with a run to the fourth round, and in the second set he began to match Djokovic from the baseline.
Golf superstar Rory McIlroy was among those enjoying the gruelling exchanges, and Tien was now winning his fair share, with Djokovic needing to come from 0-40 down to hold at 2-3.
Tien, who is working with former French Open champion Michael Chang, forced a set point at 5-4, only for Djokovic to save it with a pinpoint ace, but the Serbian may well have been in real trouble had it gone to one set all.
But he finished the tiebreak strongly and then recovered from an early break down to dominate the third set, becoming the first player in the open era to win 75 consecutive matches in the opening round of grand slams.
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