Rajput had finished second in the qualifying. Sheoran was fourth while making to the final.
Sheoran, who hails from Uttar Pradesh, got 151.6 points in kneeling, 155.1 in prone and 148.9 in the standing elimination round of the championship.
Pickl even though got 151.9 points in the kneeling rounds, he was far behind Sheoran in the prone rounds, notching up 152.1 in total - which ultimately proved to be the difference between the Austrian and the Indian.
In the standing singles shots, Sheoran struck scores of 9.3, 10.8, 9.4, 9.5 and 10.5 - a total of 49.5 as he bagged India's ninth medal in total so far in the edition of World Cup.
World No.1 Alexis Raynaud of France finished a disappointing seventh with a total of 397.7, getting eliminated after the regulation play of kneeling, prone and two series of standing.
She had earlier won two gold medals in the Women's 10m Pistol and the 10m Pistol Mixed Team events.
India remained on top of the medals standings with four Gold, one Silver and four Bronze for a total of nine medals.
China is second with two Gold, two Silver and one Bronze medal.
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