Analysts said June's hot weather had helped to lift sales at the company, which also includes Argos.
The UK's second biggest supermarket said like-for-like sales - which strip out the impact of new stores - grew by 2.3%, excluding petrol.
Chief executive Mike Coupe said he was "pleased" with the results - its best growth in four years.
Laith Khalaf, an analyst at Hargreaves Lansdown, said: "The recent heatwave helped to boost sales at Sainsbury's group, as customers turned to the Argos website to buy electric fans and paddling pools to keep cool in the hot weather."
Demand for deals on British strawberries and its summer eating range added to Sainsbury's grocery sales, which were up 3%.
Food price inflation also contributed to a rise in sales at the supermarket's checkouts.
This is the best quarterly performance by Sainsbury's in years, with sales up across the board. Like the other main supermarkets, inflation is driving some of this sales growth.
The boss said the company had managed to "keep a control over prices" and that the rise in own label goods had been a big success.
Was this a sign of shoppers trading down, for instance eating in instead of eating out? Chief executive Mike Coupe said there wasn't any evidence of a massive change in consumer behaviour although there might be a trend starting to come through.
Most striking though is the rise in clothing sales - up by more than 7%, a very strong performance, in stark contrast to its competitors on the high street. A sign, perhaps, that consumers are watching their wallets.
Mr Coupe said "inflation was coming through", but that Sainsbury's was trying to keep prices down by striking deals with suppliers.
He pointed to chicken, milk and broccoli, which he said were cheaper than three years ago.
The company's latest sales figures marked an acceleration from the previous quarter when sales grew by just 0.3%.
The growth was also slightly stronger than expected, with analysts having forecast like-for-like sales to grow 2%.
David Alexander of GlobalData, said: "Even accounting for a later Easter and Mother's Day, and the inclusion of a buoyant Argos in the figures, the numbers still present a positive picture."
Widespread media reports have suggested Sainsbury's is lining up Nisa, a convenience store chain and wholesaler, for its next acquisition.
George MacDonald, editor of Retail Week, told the BBC that Sainsbury's was "possibly grabbing on the coat-tails of Tesco which wants to buy another wholesaler called Booker".
However, Mr Coupe declined to comment on any possible Nisa deal, saying it regularly looked at potential tie-ups.
"We are not holding onto anyone's coat-tails - that's just the nature of a large corporation. Most of these conversations come to nothing," the Sainsbury's boss told reporters.
Sainsbury's has said sales of clothes, summer food and paddling pools helped speed up growth in the past few months.