World Cup silver medallist Amanpreet shot 202.2 to win the bronze in the final of men's 50m pistol at the Dr Karni Singh Shooting Ranges.
Rai could manage only 123.2 to finish last in the seven- man final.
Earlier, both cleared the qualification hurdle without much fuss.
Serbia's Damir Mikec won the gold medal with 229.3, while Ukrainian Oleh Omelchuk finished with silver after scoring 228.0 in a low-scoring but thrilling final.
Earlier in the year, Amanpreet had clinched a silver medal in the same event of ISSF World Cup Stage 1 in a 1-2 finish for India, with Rai winning the top prize then.
"Considering that this is a World Cup Final with the best shooters in the fray, you can call this as my finest performance in shooting. I'm happy but score wise it's not great, so I need to improve on that," a pleased Amanpreet said.
As luck would have it, an 8.1 in the 22nd shot for the bronze medal proved good enough for Amanpreet. In total, he shot 10 and above five times in the final.
This was India's first individual medal in the ongoing edition of the prestigious tournament.
Overall, this was the host nation's second medal in the tournament following Jitu Rai and Heena Sidhu's gold in 10m mixed air pistol on the opening day.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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