The South African, seeded 30th for the tournament, took just under two hours to subdue the 28-year-old Nielsen, who recently enjoyed some unfamiliar royal treatment when he teamed up with Caroline Wozniacki at the Hopman Cup.
But it was back to reality for the 240th-ranked Dane on Monday, as he exited his first Australian Open.
After a week of drizzle and heavy cloud cover, blue skies welcomed the players to the tournament's opening day at Melbourne Park, with temperatures rising quickly in the morning and flirting with 30 degrees Celsius before midday.
Former US Open champion Juan Martin Del Potro took a while to get going in his first-round match against French left-hander Adrian Mannarino before eventually running out a 2-6 6-1 7-5 6-4 winner in just under three hours.
While the players on court had little trouble handling the early heat, it did claim one victim during Del Potro's victory over Mannarino as the match was held up for five minutes in the second set when first aid staff were called to assist a spectator, who was taken away for treatment.