Major Nguyen Xuan Hao, a traffic police officer of Duc Hoa District of the southern province, was hit after his team signaled for the five-seat car to stop for a check.
Two people who were driving their motorbikes ahead of the car, a 29-year-old man and a 50-year-old woman, were caught in the rampage and succumbed to severe injuries.
Long An police had received tip-off that a car carrying drugs would be passing through.
Colonel Lam Minh Hong, the province's police chief, said a team of officers were patrolling in Duc Hoa District at around 5 p.m. when they saw the car speeding over.
They noticed suspicious signs and first ordered other vehicles to get out of the way.
Then they signaled for the car to stop, but it ran straight into them before flipping. The police smashed the windshield to arrest the driver and the person traveling along. They also seized several bags of drugs.
They are investigating the drug operation.
A representative of Long An Police Department told VnExpress anonymously the department's leaders have visited the three victims' families to pay condolences, and that their deaths were "very unfortunate."