Entering the event a day after claiming the 10m pistol bronze, Rai upped the ante as the final closed in on the elimination rounds.
The unassuming Army-man shot a total of 230.1, a world record, to finish on top of the podium, while Amanpreet, who was leading for a major part of the final, had to be satisfied with the silver after aggregating 226.9.
Iran's Vahid Golkhandan managed the bronze with 208.0 at the Dr Karni Singh Shooting Range.
The 29-year-old Rai was placed sixth at the end of the first two competition series of five shots each with 93.8. At that point, Amanpreet was leading the eight-man field with 98.9.
The Punjabi shooter extended his domination with a series of high scores, even as Rai tried to make his way back into contention after a start that included a horrendous 6.6, much to the disbelief of the partisan crowd.
A stunning 10.8 in one of the elimination rounds proved to be crucial for Rai, who jumped from sixth to the third position, and knocked out Kazakhstan's renowned marksman Vladimir Issachenko in the following round with a 10.5.
Rai kept up the tempo with a 10.4 and 10.0, while Amanpreet, after a fine start in his first World Cup final, suffered a meltdown.
After upstaging Golkhandan, Rai comfortably got the better of Amanpreet in the gold medal round, finishing the event with an excellent 10.5 to lay his claim on the top prize.
"It's amazing to win this gold medal here during the first combined World Cup held here in India, in front of my supporters. It's a great honour and a true emotion to see the Indian flag atop the podium," said Rai.
Thanks to another poor start, Rai had to be on his guard to avoid elimination in the following competition shots. He then got his act together and shot his way into medal contention with a series of good scores.