Julian Fellowes' drama is a major hit in the US, winning numerous Golden Globes and Emmy Awards.
Nielsen figures show ratings were 22% higher than the series three premiere.
That episode was watched by 7.9 million people in January 2013, while the third season finale was seen by 8.2 million.
That increased to 12.3 million after viewers watched the show on catch-up services over the next seven days.
Sunday night's two-hour premiere beat other high-profile dramas, including The Mentalist (9.9 million) and The Good Wife (9.2 million) on CBS and ABC's Revenge (6.7 million).
The US scheduling of Downton Abbey has grown increasingly controversial to fans because of "spoilers" from the UK, where it is broadcast several months earlier.
However, PBS president and CEO Paula Kerger said the start of the new series has become a "post-holiday tradition" for millions of US viewers.
"As this captivating drama continues, our audiences have been eagerly awaiting this new season to see what's next for these beloved characters," said Kerger.
Written by Jullian Fellowes, the drama debuted on British TV screens in 2010 and has since been sold in more than 220 territories.
The UK's most recent episode - the Christmas special - was watched by 6.6 million on Christmas Day on ITV, rising to 9.4 million once catch-up services including ITV player were taken into account.
It featured Oscar-nominated US actor Paul Giamatti as the "maverick playboy" brother of Lady Grantham and son of Martha Levinson - a role reprised by Oscar-winner Shirley MacLaine.
Series four achieved an average of 11.8 million viewers in the UK and a fifth season has already been confirmed by Carnival Films and ITV, which is expected to air later this year.