The supermarket chain grew sales, excluding fuel, by 2.1% on a like-for-like basis for the quarter ending 7 January.
Sainsbury's increased market share by driving up transactions by 1.5 million to 26 million in the period, pushing up total sales for its third financial quarter by 4.5%, excluding fuel.
Justin King, chief executive at Sainsbury's, said: "This was a strong quarter, rounded off by our best Christmas ever, despite the economic backdrop.
"Across the quarter, customers chose Sainsbury's to help them 'Live Well for Less', taking advantage of our great value offer during October and November, and then treating themselves and their families over the holiday season."
Sainsbury's replaced its 'Try Something New Today' positioning with the 'Live Well for Less' strategy in September, in an effort to reflect the increasing economic pressures on customers.
The following month it rolled out its Brand Match initiative across the UK, which ensures customers can buy branded goods at the prices offered by Asda and Tesco if they cost less at these rivals.
Sainsbury's says 'Brand Match' has proved a "big hit" and has consequently extended the initiative into 2012.
Total sales for the period were driven by Sainsbury's aggressive expansion plans, which included opening its 1,000th store, as well as 21 new convenience stores.
A 20% increase in online sales also contributed to the supermarket chain's record-breaking Christmas, with almost 75% of online merchandise orders at Christmas being "click and collect".
During the latest quarter, Sainsbury's grew its Taste the Difference range by 10%, while also seeing growth in its Basics range as a result of the growing popularity in home baking.
The supermarket also claims sales of its TU clothing range have grown market share after the launch of the Christmas partywear range of celebrity Gok Wan, which was rolled out on 17 November.
Sainsbury's success is in stark contrast to the forecast for Tesco by the latter's house broker Deutsche Bank of a 2% drop in sales for the six weeks to 7 January.
Follow Matthew Chapman at @mattchapmanUK