Stefanidi, a 26-year-old who lives in the United States, shouted in ecstasy as she cleared the bar at 4.85m and celebrated before she even landed.
Her gold was Greece's first in athletics since the Athens Games in 2004.
"I can't believe what's happened. It's amazing, the crowd were amazing, my parents are here," Stefanidi told reporters. "I'm glad to make my country proud."
Morris, 24, also cleared 4.85 but took silver because of more failed attempts earlier in the competition.
In a show of sportsmanship, she could be seen clapping along with the crowd as Stefanidi prepared for her final, ultimately failed, attempt.
Usain Bolt (JAM) of Jamaica celebrates with Pole Vault gold medal winner Ekaterini Stefanidi
Image credit: Reuters
New Zealand's Eliza McCartney, 19, cleared 4.80m to tie her national record and take bronze.
American Jennifer Suhr, 34, who won gold in London in 2012 and silver in Beijing in 2008 competed despite fighting illness since arriving in Rio.
She successfully completed only one vault, at 4.60m, after her husband and coach Rick Suhr reported on Twitter on Friday morning that she had woken up "coughing up blood."
"After warm-ups, everything just shut down. My muscles, I've never had them shake. I don't' know what happened," Suhr said as she fought back tears.
"It is such a crappy feeling to know you have worked for years for this and this to happen. It's embarrassing."
The competition came hours after Russian two-time Olympic champion Yelena Isinbayeva, who was barred from competing, announced her retirement and said whoever won would not have earned "a proper gold medal" due to her absence.