Asda's chief executive Andy Bond reported a 7.2% rise in underlying sales in the 12 weeks leading up to December 31 against Tesco's 2.5% increase in the seven weeks leading up to January 10.
Bond said that Asda had beaten its sales and profit plans with like-for-like sales for the full year up 6.5% and had gained 800,000 new customers during 2008.
Walmart, Asda's parent company, also reported better than expected results, with its US discount stores accounting for about 50% of all US retail growth during 2008 as its profits hit $13.4bn (£95m).
While rival supermarkets have reported a trend for "trading down" with consumers switching to own-label products, Asda said that sales of branded products were growing faster, up 10% in the past three months compared to 8% for private label products.
People appear to be returning to old favourites in the recession with sales of Bisto and Bird's custard powder showing some of the fastest growth, up 20%.
The supermarket also revealed that it is planning to bring back its famous pocket tapping ads, after nearly two years.
The ads which always ended with a gentle pat of the pocket and a jingle of coins have featured celebrities including Leonard Rossiter, actress Julie Walters and 'X-Factor' judge Sharon Osbourne.
Asda has promoted its marketing director Rick Bendel to chief marketing officer as part of a senior management restructure.