The little-known Spaniard, ranked No 403 in the world, reached the 17th tee needing two more birdies to set a Tour record in the co-sanctioned Tshwane Open.
However, he narrowly failed to chip in from the edge of the penultimate green before posting his only bogey of the day at 18, as he carded a 62 at Pretoria Country Club.
The 22-year-old, who is mentored by two-time Major winner Jose Maria Olazabal, fired nine birdies in his first 16 holes, including five in a row from the eighth.
And Otaegui said: “I was focused and didn’t know that I had made five birdies in a row.
“I was playing well and made a few putts, and that’s all I was thinking about. The best golf is when you think as little as possible, and this was one of those days.”
Otaegui won the 2010 British Boys Championship but is yet to post a top-three finish on the European Tour.