The mission included four space walks and the installation of a two-tonne addition to the International Space Station.
Discovery carries enough supplies to stay in orbit till Saturday, but NASA flight rules call for reserving that day in case of an unanticipated orbiter systems glitch or malfunction.
Sunita, who arrived at the station with the STS-116 mission, replaced European Space Agency Astronaut Thomas Reiter on the Expedition 14 crew at midnight on December 12.
Bob Curbeam and Christer Fuglesang began their spacewalk, the second of their 12-day space shuttle mission, at 1.41 pm CST, and finished a full hour earlier than scheduled.
The airlock at the lower pressure protects against decompression sickness, commonly called "the bends," as the two go to the even lower pressure of spacesuits on Tuesday.
Trained to remain aboard the space station until July, Williams will also join space station commander Mike Lopez-Alegria for three spacewalks early in 2007.
NASA says the Discovery shuttle will be on the most complex mission yet -- to give the International Space Station a new electricity system. The STS-116 will drop off Sunita for a six-month stay at the space lab.