Baker, who has been competing in her first ever Paralympic Games, won gold in the Grade II individual dressage event, while Napel secured silver.
"Natasha has ridden really, really well," Napel told The Guardian. "It's a battle in the arena but we are very, very good friends, I like her very much and she is a brilliant rider. I'm so happy for her to get the gold medal. I didn't lose gold, I won silver, and I'm very proud of that."
Napel has finished second to Baker twice in the London Games.