All eyes were on Koepka at the first Rolex Series event of the 2020 Race to Dubai as he made his competitive comeback after three months out with a knee injury but it was Paratore and Norris who produced impressive birdie runs to get to eight under.
Paratore finished his round with four gains, while Norris picked up seven shots in nine holes from the eighth to sit two ahead of Koepka and Australian Jason Scrivener.
Paratore has made a bright start to the season as he looks for a second European Tour title, losing out in a play-off at the AfrAsia Bank Mauritius Open.
The Italian birdied the first, second, fourth and sixth and, when he recovered from a dropped shot on the seventh with a birdie on the tenth, he was in a seven way tie for the lead.
A run of four pars saw him drop out of that group but he produced his big finish to lead by two midway through the day.
"Today the short game was really good and also the iron play," he said. "The last four holes I holed some good putts on 18 and 17 so I'm pretty happy with the short game today."
Norris was 168th in the Official World Golf Ranking after missing the cut at the Fujisankei Classic on the Japan Golf Tour in September but since then he has risen to 60th with a win, four second places and four other top tens in his last 14 events worldwide.
It has been a difficult time off the course for the South African after his father sadly passed away in July but with his brother now on the bag, he is enjoying his golf and carded his lowest European Tour round to par.
"It's been a rough year last year after losing my father," he said. "I had my brother come back on the bag again and it feels like everything is just working at the moment.
"We're having a lot of fun out there, that's the main thing, I'm really happy with what is happening at the moment."
After birdieing the second and third, Norris bogeyed the seventh but then came to life, making four birdies in a row and adding a hat-trick from the 14th to join Paratore at the summit.
Koepka started as he meant to go on, taking advantage of the par five tenth and bookending his first nine with another gain at the par five 18th.
In between he played an excellent tee shot at the par three 15th and chipped in on the 17th, adding further gains on the second and third.
Scrivener was also bogey free, starting with a hat-trick of gains and adding further birdies on the sixth, 13th and last.
Garcia and Cabrera Bello have both previously tasted victory in the Middle East and Garcia dropped a single shot on his final hole, with Rolex Series winner Cabrera Bello adding seven birdies to two bogeys.
Kitayama was bogey free, Lombard and Li dropped a single shot, and Murray had eight birdies and three bogeys.