Ko lacked her usual precision from the outset, finding a fairway bunker with her first shot. She said she felt fine as she arrived at the course but the occasion hit her soon before teeing off.
"The first of anything is the most memorable and it stays with you forever," she said.
"Just to know that I'm officially an Olympian and finished my first round as an Olympian, I think is great."
The 19-year-old missed several fairways while her approach play left her with few realistic birdie chances on the front nine.
Successive bogeys on the third and fourth holes were followed by a birdie on the sixth as Ko floundered to 28th in a 60-woman field at the turn.
Two pinpoint approach shots on the 10th and 11th resulted in birdies before a dropped shot on the 13th was more than atoned for by her spectacular nine-iron two holes later.
Ko described much of her front nine as a scramble so was pleased to finish well in contention, describing her eagle as a relieving moment as it lifted her out of the middle of the pack.
"I think it's a solid start to the first round of the Olympics.
"I tried to enjoy it. At this moment what I'm feeling, it's never going to come back again." Ko was in the last group to tee off at the Marapendi course but the wind wasn't the factor she had feared it might be.
She says low-scoring will be difficult if the wind picks up and three greens continue to harden.