The 36-year-old, whose European tour breakthrough came with victory in the 2023 Scandinavian Mixed, aced the 179-yard second in soft, calm conditions at the Durban Country Club on Friday, before repeating the feat at the 149-yard 12th.
It's estimated the odds of making two holes-in-one in the same round are 67 million to one.
At one stage, Whitnell, who immediately followed his first ace with an eagle, needed birdies at his final three holes to card a 59, but that quest fell apart after he flew the 16th green.
In attempting to chip in for birdie from an awkward side-hill lie, the clubhead slid completely under the ball and moved it only a couple of inches and he took another three shots to get up and down for a double-bogey six.
He still signed for a nine-under 63, having shot a level-par in the first round.
Although the odds of double aces are high, there have been a number of instances of them occurring.
Fellow Englishman John Hudson registered two at the European Tour's Martini International at Royal Norwich in 1971.
Brian Harman, who would go on to become Open champion in 2023, became the third man to achieve the feat on the PGA Tour with two aces at The Barclays in 2015.
Last year, Frank Bensel Jr made back-to-back holes-in-one during the second round of the US Senior Open in Rhode Island.
"I hit a flush seven-iron on the second and I didn't realise it had gone in until down the bottom they cheered," Whitnell, who took 11 years to earn a full European tour card after turning professional in 2009, said in his post-round interview.
"It's a weird feeling. Obviously, the adrenaline is pumping but you have to focus on your job and I managed to do that today.
"I've never had one in tournament play. I've had one in practice at Le Golf National in Paris - but to have two in one day is pretty special.
"I've had everything today: an air shot, two bogeys, a double, three eagles and I've come out nine-under par, so I can't complain."
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