The "big four", which includes market leader Tesco, Wal-Mart's Asda and Morrisons, are being squeezed between hard discounters Aldi and Lidl and upmarket players Waitrose and Marks & Spencer.
Market researcher Kantar Worldpanel said Sainsbury, battling Asda to be the UK's second-biggest grocer, grew sales by 3.1 percent in the 12 weeks to Jan. 5, outperforming overall grocery market growth of 2.9 percent and maintaining its market share of 17.1 percent.
Market leader Tesco saw sales rise 0.2 percent and its share dip 0.8 percent to 29.6 percent.
Asda's sales rose 0.8 percent, while Morrisons' fell 1 percent.
Aldi, Lidl and Waitrose saw sales increase 29.4 percent, 17.5 percent and 6.4 percent respectively.
Last week Sainsbury's posted a positive update for its third quarter, while both Tesco and Morrisons revealed sales falls in the Christmas period and saw annual profit expectations reduced.
Also last week Aldi and Lidl said they had enjoyed record Christmas trading, without disclosing figures, while Waitrose and Marks & Spencer's food business reported positive figures.
The Kantar data also showed Internet grocery sales over the Christmas/New Year period grew 22 percent year-on-year with 15 percent of British households placing orders. It said grocery inflation was 2.5 percent for the 12 week period, the lowest level since October 2012 which offers a small respite for hard-pressed household budgets.
Kantar Worldpanel - Market share (percent)
