The Spaniard held a share of the lead at the halfway stage but reeled off four birdies in the first six holes on Saturday to give himself breathing space at the top.
He bogeyed the seventh but bounced straight back with a birdie on the eighth before having to wait patiently for his next gain, which arrived at the 16th.
Otaegui then made further birdies at the 17th and 18th to head into Sunday's fourth round on 16 under par.
His nearest challengers were countryman Angel Hidalgo and Swede Joakim Lagergren on 10 under following their rounds of 70 and 67 respectively.
Australia's Min Woo Lee was another shot back in fourth, two ahead of fifth-placed Robert MacIntyre, with the Scot making three birdies and a solitary bogey in his 69.
Otaegui was pleased with his performance, saying: "I'm very happy, everything went perfectly today. I putted well, I felt very comfortable.
"The crowds were pushing amazingly, so that was unbelievable.
"I had a very good start with a nice birdie on the second and then three birdies in a row at four, five and six and that gave me a bit of momentum.
"I felt good on the course, tried to enjoy it, tried to stay focused. I missed a couple of birdie putts at the beginning of the front nine but finished with three good birdies."