The South African pair both made an eagle on Thursday morning, with Norris adding six birdies - including three in a row from the third - in a flawless first round.
Nienaber, meanwhile, made the most of his immense power as he carded an eagle, nine birdies and three bogeys to get to eight under par.
None of the afternoon starters were able to catch the early clubhouse leaders, but 64s from American Johannes Veerman and Canada's Aaron Cockerill took them within a single shot of the summit.
Richard McEvoy, Rhys Enoch, Gonzalo Fernández-Castaño, Adilson da Silva and Benjamin Follett-Smith were another stroke back on six under.
Nienaber, who won the 2019 South African Amateur Championship before turning professional last year, is playing in his 11th European Tour event since the restart in July this week.
He has recorded two top tens during that run, with his best result a fourth place finish at the English Championship in August.
The 20-year-old started his round with a par at the tenth and would have to wait until he reached his back nine for his next par as his round got off to a lively start.
After notching a birdie on the 11th, Nienaber made an eagle at the long 12th before picking up further shots at the 13th and 14th to reach five under after just five holes.
Back to back bogeys on the 15th and 16th threatened to stall his momentum but he bounced back with a birdie at the 17th before rolling in from 20 feet on the 18th to close his front nine with another gain.
Nienaber nearly holed his second shot for an eagle at the par four third but had to settle for a tap-in birdie.
One of many highlights of Nienaber's opening round came at the long fourth, where he sent his tee shot a whopping 439 yards before knocking his approach to five feet.
The eagle putt hit the hole but did not drop in, so he walked off the green with a birdie.
Nienaber continued to make plenty of chances, narrowly missing birdie tries at the fifth and sixth before holing from 15 feet at the seventh to get to eight under.
After failing to get up and down for par at the short eighth, Nienaber finished his round with a birdie from five feet on the ninth.
He said: "Eight under is nice around any golf course and to do it here in the first round of the Joburg Open, being back home again, is great.
"I haven't played much in South Africa since I turned pro but it's been great to be home.
"I'm just looking forward to the next three days and the next two weeks after."
Local lad Norris reached the turn in 33 after making an eagle on the 12th and a birdie at the 14th.
He then finished his round with a flourish, following up a hat-trick of birdies at the third, fourth and fifth with further gains at the seventh and ninth to join Nienaber at the summit.
"I've been hitting the ball nicely for a couple of months now, so it's been good," said Norris.
"I'm enjoying my couple of weeks back home, playing my home course, putting some low scores out there and just building some confidence before this.
"It's nice to put a low score out there. The course is looking good, so just take it on. You've got to give yourself opportunities and go for it.
"I had a sound game plan set to know when to attack and when to back off."
After beginning his round with a bogey on the first, Veerman responded in style, making a bounce-back birdie at the second before reeling off a hat-trick of gains on the fourth, fifth and sixth.
He closed the front nine with another birdie and continued to impress after the turn, picking up shots at the 12th, 14th and 18th and producing good par saves on the 15th and 17th to keep his round going.
Starting at the tenth, Cockerill fired back to back birdies on the 12th and 13th to turn in 34 blows before making gains at the first, third, fourth, seventh and eighth to join Veerman on seven under.