The communist neighbours have traded accusations over the May 26 sinking incident, with Hanoi decrying an "inhuman act" by China, which blamed intrusion by the Vietnamese vessel.
The video images, shot from a nearby Vietnamese vessel, show a much larger Chinese ship racing after a small wooden Vietnamese fishing boat, ramming into it and causing it to tip over and sink.
Vietnamese officials have said the 10 fishermen on board were rescued by nearby vessels after the incident, which occurred about 12 nautical miles southwest of the oil rig.
An additional 12 fishing vessels have been damaged, according to Ha Le, deputy head of Vietnam Fisheries Surveillance Department.
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"They were prevented from fishing, threatened by Chinese vessels, had their equipment destroyed and the crews were brutally treated," he said.
Relations between Vietnam and China have plummeted over the oil rig's presence, which has worsened an increasingly heated dispute over territorial claims in the area.
"Every day, China has between 30 and 137 boats around the oil rig, including six warships," said Ngo Ngoc Thu, the deputy commander of the Vietnam Coast Guard.
"Vietnamese ships are being restrained... And trying to avoid China's ramming," he said, adding that Vietnam had not been using water cannon against Chinese boats.
Tensions over the oil rig sparked violent anti-Chinese riots in Vietnam last month. Beijing says four Chinese citizens died in the unrest, while Vietnam says three Chinese died.
China claims nearly all of the South China Sea, even waters approaching the coasts of its neighbours, and has become increasingly assertive in staking those claims.
Vietnam, the Philippines, Brunei, Malaysia and Taiwan have competing claims to parts of the sea.