Djokovic had to call for a medical time-out just five games into the contest inside Arthur Ashe Stadium, when a trainer massaged the upper part of his right arm.
The Serbian, who has admitted an injury to his left wrist has also not healed, looked uncomfortable throughout but he did enough to beat Janowicz 6-3 5-7 6-2 6-1.
He now faces Czech Jiri Vesely in round two and after the match the world number one was reluctant to discuss his physical issues.
“It’s getting better and better each day,” Djokovic said. “I’m glad that I’m experiencing that. So hopefully as the tournament progresses, I’ll reach my peak.”
On calling for the medical time-out, he said: “It was just prevention. It’s all good.”
Janowicz was too careless to capitalise on any weakness in his opponent’s armour but Djokovic will have to survive tougher tests if he is to win his 13th grand slam title in New York.
Vesely can be a dangerous opponent while Marin Cilic, Jo-Wilfried Tsonga and John Isner all lie in his quarter.
“To be honest, I take it day by day. That’s what I feel at the moment,” Djokovic said.
“It’s good, as I said, just to finish the match. I’m pleased that as the match progressed I was feeling better and better.
“Tomorrow is a new day. I hope that I’ll feel overall good so I’m able to perform at my best for the next match.”
Rafael Nadal is a potential foe in the semi-finals and he appeared far less troubled by his own wrist injury as he cruised past Denis Istomin 6-1 6-4 6-2.
The Spaniard will now face Andreas Seppi in the second round at Flushing Meadows after the Italian overcame Frenchman Stephane Robert.
Nadal played with his troublesome left wrist heavily bandaged and, while he seemed unrestricted, hitting 14 of his 21 winners off the forehand, the 30-year-old said he still lacks confidence on that side.
“I am hitting very well the backhand, but it’s true that the forehand I need time. I need confidence and I need to keep practicing the forehand,” Nadal said.
“It’s not easy to go two months and a half out of competition in the middle of the season without hitting a forehand. I need to have the confidence again with my wrist.
“That is coming, because I feel the wrist much better. That’s very important thing for me. The most important thing.”
Elsewhere, on Monday, John Isner won an epic all-American clash with the talented 18-year-old Frances Tiafoe. Isner came from two sets down to triumph 3-6 4-6 7-6 (7/5) 6-2 7-6 (7/3).
Milos Raonic, Cilic, Gael Monfils and Tsonga are also safely through.
Two-times grand slam winner Stan Wawrinka dealt Fernando Verdasco a rare first-round loss at the US Open last night, sweeping aside the Spaniard in straight sets.
The third-seeded Swiss dominated the left-handed Verdasco with his punishing groundstrokes to claim a measure of revenge with a 7-6(4) 6-4 6-4 victory at Arthur Ashe Stadium.
Verdasco, ranked 46th, had won 12 of his 13 previous first-round matches at Flushing Meadows.
Wawrinka, winner of last year’s French Open and the 2014 Australian Open, had trailed Verdasco 3-2 in head-to-head action after falling to the Spaniard in straight sets in the first round this year at the Queen’s Club run-up to Wimbledon. Meanwhile, Garbine Muguruza had to come from a set down and fight off a bout of illness as she battled past Belgium’s Elise Mertens at the US Open.
Muguruza told a doctor she was having trouble breathing after losing the first set 6-2 but she recovered her fitness in Louis Armstrong Stadium to win 2-6 6-0 6-3.
The Spaniard, who won the French Open earlier this year, will now face Latvia’s world number 48 Anastasija Sevastova in round two.
Second seed Angelique Kerber is also through after her opponent Polona Hercog retired injured while last year’s finalist in New York, Roberta Vinci, beat Germany’s Anna-Lena Friedsam in straight sets.
Muguruza is considered one of the few players capable of challenging Serena Williams at Flushing Meadows, but the 21-year-old looked in trouble at the end of the opening set.
“I started and it was difficult a little bit to breathe for me,” Muguruza said. “It was really humid. When you feel the heat it makes you a little bit down.
“I forgot that there was the ice towels and everything. So I start using them, trying to breathe a little bit better, taking more calm just to go with the match.
“But I didn’t remember that it was that hot in here.
“I don’t know why I felt this today. It was like really, really humid.”