The home favourite started the day two shots off the lead but carded six birdies and a single bogey to be the only player at ten under after 36 holes at Leopard Creek Country Club.
England's Marco Penge was then at nine under after matching the lowest round of the day with a 66, one clear of countryman Paul Waring and South Africans Christo Lamprecht, Charl Schwartzel and Robin Williams.
Jarvis only turned professional in August 2022 but quickly impressed, securing a top ten finish in the 2023 edition of the Joburg Open.
A win at the Euram Bank Open and three runner-up finishes helped him finish second on last season's Road to Mallorca and he has made the cut in both of his appearances so far in his debut campaign on the DP World Tour.
That does not tell the full story, though, as he entered Saturday at the Joburg Open in a tie for 17th and was just one off the lead after 36 holes at last week's Investec South African Open Championship.
He fell back to finish outside of the top 35 at both of those events and will now be looking for a successful weekend as he hunts a maiden DP World Tour title.
"I keep learning out here as the weekends go by," he said. "I'm just trying to stay patient at the moment and learn as much as I can.
"I'm really looking forward to the weekend. It's a great place to be, I love being in the bush so I can't wait.
"The game is feeling really good. I didn't have the weekend I wanted last weekend but hopefully it's a bit different this time around. I'm hitting the ball great so I've just got to keep doing what I'm doing and hope it pays off.
"I played really nice today, managed my game really well and I'm pleased with the score at the end."
Amateur Lamprecht and Waring had set the target in the morning and Jarvis set about overhauling them as he birdied the first, third, sixth and eighth to turn in 31 and share the lead with Schwartzel.
A chip-in on the tenth had him ahead by two as the four-time champion slipped back but Penge - who finished once place above Jarvis to win last season's Road to Mallorca - was on the move.
After starting on the tenth, he birdied the 12th and 13th, made an eagle on the par-five 15th and holed a long putt on the 18th to get to eight under.
Further gains on the sixth and eighth had him in a share but he dropped a shot on the ninth, only to see himself back at the summit as Jarvis made a first bogey of the day on the 17th.
The 20-year-old hit straight back, however, laying up and putting his third to three feet at the par-five last to lead the way.
Schwartzel had picked up five shots in six holes from the sixth to join the lead but made bogeys on the 13th and 14th before birdieing the 15th in a 68.
Lamprecht did not feel at his best but a 69 containing six birdies and three bogeys was enough to hand him the lead early in the day.
Waring then joined him at the summit with a 68 containing one more birdie, while overnight leader Williams made four birdies and three bogeys in a 71.
Home favourite Kyle Barker, English pair Sam Bairstow and Andy Sullivan and Spaniard Manuel Elvira completed the top ten at seven under.
Former champion Christiaan Bezuidenhout made the fifth hole-in-one of the season with a 151-yard wedge at the fifth to sit in the group four shots off the lead.