The 31-year-old went one better than her sixth place finish in the event at the Tokyo 2020 Paralympic Games.
Given the quality of the display, it bodes well for her remaining three events at Paris 2024.
Her all-round performance underlines her current form as she registered her two fastest ever times for the event at the Velodrome de Saint-Quentin-en-Yvelines.
Victory was secured by Caroline Groot of the Netherlands, who struck gold in 35.566sec.
That was slightly slower than the world record of 35.390sec which she set in qualification.
Silver went to Marie Patouillet of France, with bronze secured by Kate O’Brien of Canada.
Defending champion Kadeena Cox of Great Britain crashed out on the opening bend of the final.
An elated Murray, who also competes in the women’s C5 3000m individual pursuit on the track as well as on the road in the women’s C5 time trial and women’s C4-5 road race later, said she was thrilled with her performance.
"I am blown away I got to the final," she said in a press release.
"It was a stacked field, and the time trial is definitely not my best race, so just to make the final is incredible."
But he had his good friend, former Liverpool football club manager Jurgen Klopp, watching from the stands cheering him on.
The 44-year-old is a seven-time Paralympic medallist in athletics for Germany. He only took up badminton three years ago and had the misfortune of his prosthetic breaking just prior to the game.
But he put in a whole-hearted effort. Ultimately, however, his more experienced British opponent prevailed 21-5, 21-2.
"Daniel was simply stunning today," Czyz said.
"I tried everything. I tried to put variation in my shots, but he had an answer for everything.
"Daniel is a great athlete, and I am sure he will be fighting for the gold medal."
