It said the level of the lake had dropped by eight metres in the space of three hours.
The lake is the largest of the more than 30 created when landslides from the devastating quake on May 12 blocked the flow of rivers in the region.
Water was draining out nearly 60 times faster than it was flowing in following the removal of debris, Xinhua said.
The breakthrough came after Chinese soldiers resorted to firing a series of battlefield missiles at boulders that were blocking the path of one of the channels.
Muddy water released from the lake rushed into the devastated town of Beichuan, covering about a third of the settlement with the waters continuing to rise.
The town - where more than 8,600 out of an estimated population of 13,000 were killed - was evacuated in the aftermath of the quake.
Authorities warned last week that more than a million people were at risk if the lake had burst its banks.
About 250,000 residents in most imminent danger have already been evacuated.
Draining the lake has been one of the Chinese government's top priorities as it continues a huge recovery operation in the aftermath of the earthquake.
Authorities announced on Tuesday that they had chosen a new site to rebuild Beichuan town, 35 km from the original one.
According to the latest figures, the quake killed 69,142 people with more than 17,000 still listed as missing.
Dealing with the estimated five million left homeless by the quake remains the biggest challenge facing the recovery effort.