The 38-year-old's battling victory under the lights of Arthur Ashe Stadium made him the oldest man to reach the last 16 at Flushing Meadows since American Jimmy Connors managed the feat at the same age in 1991.
Already the holder of the most grand slam titles (24) and match wins (395), Djokovic reached another milestone by surpassing Swiss maestro Roger Federer to become the man with the most hardcourt victories at the majors with his 192nd win.
The four-times New York winner also improved his record against Norrie to 7-0.
"I guess coming into the match, any match, you really want to win in straight sets without any drama and just ease through, but that's not possible," said Djokovic, who is playing in his first event since losing to Jannik Sinner at Wimbledon.
"My team wants me to suffer on the court so I can get some more minutes spent in match play. It's good that I get tested. I hadn't played any matches since Wimbledon and it's been for us quite a long time, five to six weeks.
"I'm still trying to find my groove and my rhythm on court," added the Serb, who said Friday's performance was an improvement on his first two matches.
"I think it was probably the best serving performance of the tournament.
Djokovic then began to feel the effects of a back problem after going up 5-4 and received treatment off the court before returning to serve out the opening set.
He called for more medical attention three games into the next set and his first-serve speed briefly dipped following that break in play.
However, he started to fire on all cylinders again before advancing.
Earlier, Carlos Alcaraz marched on at Flushing Meadows, insisting there was no need for concern after he needed treatment on his right knee during an otherwise trouble-free demolition of Italian Luciano Darderi.
After having his serve broken for the first time and also requiring the physio to treat him near the end of the second set, it felt like perhaps this could be the first wobble for the stellar Spaniard at this year's New York major.
Yet it really didn't look that way as the 22-year-old pummelled Darderi 6-2 6-4 6-0 to waltz into the fourth round while still not having dropped a set so far.
And he was quick to assure everyone after his one-hour 44-minute victory that there was nothing to worry about after he had taken a medical timeout at 5-4 in the second set following a nervous moment when he'd jolted his knee while landing awkwardly off a serve.
"I'm feeling good," he told the Arthur Ashe Stadium fans after treating them to 31 spectacular winners. "It was just a precaution that I asked for the physio.
"When he broke my serve (with Alcaraz leading 4-1 in the second set) in the last point I felt something in the knee, but after five or six points it was gone. I just asked the physio to take care of the knee, so I had to be feeling good."
So good indeed that he reeled off the last seven games after the time-out to set up a fourth-round clash with Frenchman Arthur Rinderknech, who beat his compatriot, Daniil Medvedev's conqueror Benjamin Bonzi 4-6 6-3 6-3 6-2.
In other matches, fourth-seed Taylor Fritz beat Jerome Kym 7-6 (7-3) 6-7 (11-9) 6-4 6-4 as fellow Americans Frances Tiafoe and Bryan Shelton (retired) were ousted.
Tiafoe, the No.17 seed was beaten 6-4 6-3 7-6 (9-7) by Jan-Lennard Struff while No.6 Shelton injured his shoulder against Adrian Mannarino and retired at two sets all.
There were also straight-sets wins for No.20 Jiri Lehecka and No.21 Tomas Machac over Raphael Collignon and Ugo Blanchet respectively.
with Reuters
