Locked 1-1 at the end of the regulation time, India conceded a penalty stroke three minutes into extra time, which USA captain Lauren Crandall converted easily to pocket the bronze medal at the Harbour Hockey Stadium in Auckland.
Both India and USA played a defensive game and it was the latter who took the lead in the 47th minute through a penalty corner, converted beautifully by Shannon Taylor.
Down 0-1, the Indian eves had no option but to go for the offensive. The move resulted in some good penetrations into the American circle but India's forwardline lacked finishing.
India finally managed to restore parity in the 56th minute when Chanchan Thokchom tapped the ball home after receiving a pass from Poonam Rani.
Thereafter, USA got as many as four clear cut scoring chances in the form of penalty corners but failed to convert a single one as the match went into additional time.
In just the third minute of the extra time, USA earned a penalty stroke when Shannon Taylor's direct hit from a setpiece struck India's pole player Joydeep's foot, and Crandall made no mistake in slamming home the ball.
Hosts New Zealand won the gold by beating Australia 3-2 in the summit clash.
The second leg of the Four-Nation Tournament will be played at Lloyd Elsmore Hockey Stadium in Pakuranga, New Zealand from April 18- 22.
