Viyaleta Bardzilouskaya, a Belarusian competing as an individual neutral athlete, clinched silver, while Canada's Sophiane Methot took bronze.
Page, who was fifth in qualifying, had long been on a quest for gold, having won the silver at the 2016 Rio Games and bronze at the Tokyo Olympics.
Page, the seventh of eight competitors to jump in the final, said she was extremely nervous when awaiting her score, which amounted to 56.480 points.
"I was hoping it was good enough for a medal," she said.
"I was just hoping for a medal, and then to see my name come on top of the scoreboard just meant that I had the chance to become an Olympic champion."
Page was so thrilled to see herself in first place that she thought she had already won gold.
"I forgot there was another competitor to come," she said.
Bardzilouskaya, second in the qualifications, is one of the few Belarusian or Russian athletes cleared to compete at the Paris Games.
Teams from Russia and Belarus have been banned from taking part in the Games over Moscow's invasion of Ukraine, with Belarus having been used as a staging ground.
Only certain individuals have been authorised by the IOC to compete after undergoing a screening process designed to root out anyone who has publicly supported the war or military.
