In the finals of the 50-metre pistol event, Rai missed out on the gold medal by 0.1 point having shot 193.1, after aggregating 568 in the qualification round.
The gold medal went to Serbia's Damir Mikec, who shot 568, while the bronze was won by Japanese Tomoyuki Matsuda for shooting 172.9.
The 27-year-old shooter from Lucknow had last week bagged a silver medal in the men's 10-metre air pistol event at the ISSF World Cup in Munich.
She went on to shoot a score of 185.3 in the final to clinch the bronze medal.
"This is my first ever World Cup medal and I am really happy. I must thank NRAI for their support. I also want to specially thank Olympic Gold Quest for their wonderful support to me. They have sent me quite a few times to Austria for training stints under world renowned coach Thomas Farnik which has really improved my technique," an elated Ayonika said.
"I also work with Olympic Gold Quest sports psychologist Vaibhav Agashe and sports medicine specialist Dr Nikhil Latey. They have both made a big difference to my confidence and fitness.