Rajput had finished second in the qualifying, while 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.
Meanwhile, Haryana teenager Manu Bhaker, who has already won two gold medals here, has entered the final in the women's 25m pistol.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)