The video appears to confirm Vietnam's version of the clash in the South China Sea on May 26.
It was the most serious incident between ships from the two countries since the positioning of the rig on May 1 triggered fury in Hanoi and underlined Beijing's determination to assert its sovereignty claims in the oil- and gas-rich waters.
China last week said the Vietnamese fishing vessel sank after it rammed into a Chinese ship.
The footage, shot from another Vietnamese fishing vessel, shows the Chinese boat chasing two much smaller Vietnamese ones. It then hits the back of one of them, tipping it over.
"Look, it rammed and sank it'' someone off camera shouts.
Other footage released Thursday then showed the hull of the sunken boat in the water. Vietnam previously said 10 fishermen had to be rescued from the seas, and the Chinese boat made no attempt to help.
At the briefing where the video was shown, Vietnamese officials said 24 Vietnamese boats had been damaged since the standoff began.
Massively outgunned militarily and economically intertwined with its giant northern neighbor, Vietnam has limited options in responding to Beijing. It is trying to rally regional and international support, and has said it is considering legal action against China in an international court.
Tensions between the two countries are likely to run high until Beijing withdraws the rig.
China insists it has done nothing wrong and is refusing to do that, but said when it positioned the rig that it would withdraw it on Aug. 15.
The escalation is the most serious in years between the two countries and shows the potential for conflict in the waters.
China claims nearly all of the South China Sea, bringing it into dispute with Vietnam, the Philippines, Brunei, Taiwan and Malaysia.
Southeast Asian countries have struggled to forge a common front against China, the world's second-largest economy.