Taranjit Parmar was on her way home when she got into a minor accident on Hempstead Turnpike near Gardiners Ave in Levittown on Thursday, New York Daily News reported.
Parmar and the truck driver pulled over into the parking lot of a nearby gas station after colliding, police said.
But when she got out to inspect the damage to her vehicle, the driver of the pickup truck took off and ran over Parmar while speeding away, it added.
"She had called my wife and said, 'Hi, Mom,'" Parmar's father, Ranjit Parmar said.
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"Then she said 'Oh, no, Stop!' and the call got disconnected. There was no answer after that," he added.
Medics rushed Parmar to Nassau University Medical Center, where she died from massive head and chest injuries.
Parmar, who was studying to be a dentist at Adelphi University, was 10 minutes from her home when the tragedy occurred, the report added.