JOHANNESBURG, February 9, 2014 (AFP) - Coetzee, who started the final round fours shots off the lead, closed with a 66 for a 19-under winning total.
Three shots back and in a share for second place were Justin Walters of South Africa (73) Tyrrell Hatton of England (66) and South Korean Jeong Jin (71).
Coetzee, who had finished in the top 10 on the European tour on 24 previous occasions, said he was "lost for words".
"I've been waiting a while and I started doubting, so I am very happy," he said.
"I get to share this with my family and friends and my caddy.
"It was my mum's birthday yesterday and I wanted to win it for her because I forgot to get her a present."
The win also qualifies Coetzee for the British Open at Hoylake in July.
He birdied all three par fives on the front nine, including a ten-footer at the fourth, going out in 33.
The 27-year-old took the lead for the first time at the tenth.
His victory was confirmed by a slice of luck at the 15th.
Coetzee's drive was heading towards a stream when it hit a tree and ricocheted back onto the fairway. He then birdied the hole.
Three pars at the final three holes left him waiting on compatriot Walters, who needed an eagle on the 18th, but he ended up posting a bogey.
Coetzee, who received a winner's cheque of 206,050 euros, is the sixth South African to triumph in the eighth staging of the Joburg Open.
The top three players automatically earned qualification for the British Open, with the unlucky Hatton missing out to Jeong and Walters, because of his lower world ranking.