The temporary dress code change, giving players a choice of trousers or shorts for the event in South Africa, was agreed as temperatures soared to 39 degrees celsius (102.2 fahrenheit).
South African Keith Horne, Garrick Porteous of England and Spaniard Pablo Larrazabal shared second place on 66 at the Leopard Creek Country Club in the northeast of the republic.
Spaniard Alejandro Canizares was alone in fifth place after a 67 in the first tournament of the new season, which began just four days after Spaniard Jon Rahm won the 2019 edition.
Besseling, a 33-year-old ranked 307 in the world, collected two birdies to turn in 33 over a layout rated by many golfers as the best in South Africa.
On the back nine, he recovered from a bogey four on 12 to go birdie, birdie, eagle, and another birdie at the par-five last hole completed the best round of the day.
“I played nicely,” said Besseling. “It is a great start to the season and a great round. I am very happy with my 65 today.
“I had it going nicely on the par fives. I was able to get there in two with irons and converted the birdies, and an eagle on 15 really helped.
“I played well from the start and gave myself birdie opportunities. I also had a good par-save on eight, followed by a nice birdie on nine.
“From there on, I got some better chances and some putts dropped. I am really happy with a 65 and a birdie on the last hole.”
Larrazabal carded an eagle, five birdies and a bogey, Horne seven birdies and a bogey and Porteous six birdies to lie one stroke off the pace.
Major winner Charl Schwartzel of South Africa shot a 70 in his first competitive round since suffering a wrist injury last April.
Another South African, four-time major champion Ernie Els, had a disappointing two-over 74, as did 2018 Ryder Cup captain Thomas Bjorn.
The build-up to the Dunhill, at a stunningly picturesque course bordering the famed Kruger National Park wildlife reserve, was dominated by the agreement to allow shorts.
There was a mixed reaction as many players stuck with trousers while the majority of South Africans, including Els, favoured shorts.
“It was awesome playing in shorts,” said South African Branden Grace, who opened with a 68 on the 6,627-metre (7,249-yard) track.
“The decision was spot on because it was boiling out there. I just hope none of us suffer from sunburn.”
Larrazabal opted for trousers, saying “I did not feel like wearing shorts today although it was extremely hot throughout the round.
“I have experienced more extreme heat in European Tour events, especially in Singapore and Malaysia.”