The world number 545 holed out from 185 yards with a seven iron on the par-three second hole before repeating the feat with a wedge shot on the 128-yard 12th.
Australian Andrew Dodt is the only other European Tour golfer to have multiple holes-in-one in a round - at the 2013 Nordea Masters.
Whitnell, 36, had never had a competitive hole-in-one in his previous 153 tournaments on tour.
"Coming back after this morning I was struggling to make the cut, so I knew I needed to go out and play well," he said.
"It is a weird feeling, everything in one. You are obviously excited and your adrenaline is pumping but at the same time you have got to focus on your job but I managed to do that."
Whitnell also eagled the par-five third and was five-under-par through three holes.
He needed to finish with three straight birdies to post a 59, but had an air shot en route to a double-bogey on the 16th.
A crazy nine-under-par second round of 63 featured three eagles including the two holes-in-one, seven birdies, one double-bogey and two bogeys.
Whitnell sits five shots behind leader Shaun Norris of South Africa at the halfway stage in Durban.