The South African will compete at Royal Liverpool in July alongside joint runners-up Justin Walters, also of South Africa, and South Korea's Jeong Jin.
Walters had held the overnight lead alongside compatriot Thomas Aiken, but neither could break par in their final rounds. That left the way open for Coetzee to claim his first European Tour win.
Places at the Open Championship were available to those who finished in the top three at the Royal Johannesburg and Kensington GC. Tyrell Hatton of England was one of those out of luck despite also finishing on 16 under. He misses out as his world ranking of 276 is lower than those of Walters and Jeong.
Further words of exasperation were delivered with a Scottish accent; Alastair Forsyth and Craig Lee both falling away yesterday having been tied for the lead after the opening round of the tournament. Forsyth, who was still in contention going into the final round, could manage only a 76 and finished 10 shots off the pace on 278. He had been level with Coetzee going into the final round but his joint 31st-place finish still earned him €10,400 as leading Scot. Lee, who was still leader at halfway, followed his third-round 74 with a 75 to finish joint 49th on 281.
Coetzee started the day four shots off the lead but birdies at the first, fourth, sixth and eighth holes enabled him to move into the lead. He picked up a further shot on 10 and another birdie at 15 helped him to a flawless six-under-par round and a three-shot victory.
"I don't know what I'm feeling," said Coetzee, who was home favourite as the tournament got under way. "I'm lost for words. I've been waiting a while and I started doubting, so I'm very happy. I got to share this with my family and my friends. It was my mum's birthday on Saturday and I wanted to do it for her as I forgot to buy her a present."
Hatton also shot 66 as he recovered from a bogey on the par-3 second to ascend the leaderboard with seven birdies, including a pair on 17 and 18. It was more frustrating for Walters, though, as he never really got going in his round and a bogey on the par-five eighth dropped him back to level par for his round. Two more dropped shots and a birdie followed on the back nine as the 33-year-old ended his week with a 73. Jeong recorded a one-under-par 71 after reaching the turn level and picking up a shot on the back nine.
Aiken was left frustrated by his inconsistency as he picked up four birdies but gave back six shots, including four on the back nine, to finish with a 74. That left him four shots off the lead. Also on 15 under was England's Andy Sullivan who recorded the best round of the day with a 65.
Alvaro Quiros and Matthew Baldwin were also in the group on 15 under. Ross Fisher, the former Ryder Cup player, was among a larger group on 13 under.