Total sales were up 6.7 per cent, excluding petrol, for the 12 weeks to June 17.
The group has not recorded like-for-like increases as high since Christmas 2002, but those figures were compared to an average market growth of 6 per cent. Today's results compare to a market growth rate of about 2 per cent.
It is the supermarket group's sixth consecutive quarterly like-for-like sales increase and shows a growth rate ahead of Tesco - the UK's number one supermarket chain unveiled first-quarter UK like-for-like sales rises of 4.5 per cent last week.
Tesco's results do not cover the lucrative past two weeks, in which warm weather and the World Cup have boosted sales across the sector. However, Sainsbury's chief financial officer Darren Shapland said that excluding the football effect, Sainsbury's underlying like-for-like increases were about 5.2 per cent, still ahead of Tesco.
Sainsbury's chief executive Justin King said: 'The results demonstrate good strong momentum. We have continued to grow sales ahead of the market and our recovery remains on track. We are now providing a much better and more consistent shopping experience.'
King said Sainsbury's strong sales performance had enabled it to cut the prices of groceries, citing a price deflation figure of 0.9 per cent.
The supermarket is looking at its non-food supply chain, switching from using agents to direct buying. It opened buying offices in Poland and Hong Kong earlier this year, but it will be Christmas next year before the results are seen in-store. Food remains the group's focus, with non-food representing just 7 per cent of the mix.
During the quarter, the grocer opened four convenience stores, taking its total number of outlets to more than 300.
The group is in its second year of its Making Sainsbury's Great Again turnaround plan.