The men were convicted yesterday in the southern province of Binh Duong, where much of the destruction and looting was concentrated, in public outdoor trials attended by thousands, the Thanh Nien newspaper said.
Le Van Nghiem, 23, was sentenced to three years in prison for "causing public disorder" and property destruction during the May 13 violence.
He had joined hundreds of rioters in pulling down a factory gate and destroying a police car, it said, adding that he confessed to the crimes and expressed remorse.
They are the first known convictions linked to the riots.
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The trials were held outdoors on the grounds of two separate government building. Vietnamese authorities occasionally hold trials in public to act as a deterrent, especially in high-profile cases.
China moved the giant oil-drilling rig into disputed waters in the South China Sea early in May.
Dozens of vessels from each side have engaged in a tense and ongoing confrontation.
China -- which has evacuated thousands of its nationals from Vietnam over the riots -- says four Chinese citizens died in the violence, which targeted foreign-invested factories and other businesses. Vietnam says three Chinese were killed.
Asked about the convictions, China's foreign ministry spokesman Qin Gang said more needed to be done.
"We have noted the report that two men have been given jail sentences. But we think this is not sufficient," he said today.
"We call on Vietnamese authorities to carry out a thorough investigation into the case, strictly punish the criminals and compensate Chinese firms for their losses."
Vietnam says hundreds were detained over the riots and have vowed stiff punishment. Many more trials are expected.
The government also said it would assist riot-hit companies -- many of whom saw their premises destroyed -- with tax breaks, rent waivers and lines of credit.