The Zug, Switzerland-based company said the drillship Dhirubhai Deepwater KG1, working for India's ONGC, beat a prior world record set by the same rig in February in 10,385 feet of water.
Last May Transocean signed a deal worth $432 million in shares to buy out the Dhirubhai Deepwater KG1 and sister unit Dhirubhai Deepwater KG2 from a 50-50 joint venture with Quantum Pacific Management.
The 2009-built Dhirubhai Deepwater KG1 was constructed at South Korea's Samsung Heavy Industries.
It is sublet to ONGC under a Reliance Industries contract that runs through July 2014 at a day rate of $510,000.
The drillship is equipped to operate in up to 12,000 feet and drill to as deep as 35,000 feet with the capacity for a 172-person crew, according to Transocean.
Company shares were trading up 1.74% in New York as of early afternoon Monday.