The rate of growth in grocery sales slowed over the three months the end of October according to figures compiled by market research firm Kantar Worldpanel.
Sales were 0.6% higher than in the same period in 2012, the slowest annual growth rate since June.
Dunnes Stores appears to have benefitted from its recent "shop and save" advertising campaign.
The retailer boosted sales by 5% during the quarter, compared to the same period in 2012, and added one point of market share to 23%.
David Berry, commercial director with Kantar, said the leading grocery chain - Tesco - continues to feel the competitive pressure.
Dunnes and discounters Aldi and Lidl are both growing sales and market share at Tesco's expense.
"Tesco continues to feel the pressure, with sales declining by 6.5% and its market share dropping from 28.6% last year to 26.6% now. This is the twelfth successive quarter of decline for Tesco, which has lost significant market share to the discounters over the course of the year," he said.