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.

Jodie Simpson, 38, fell into a vegetative state after taking an overdose of drugs at her home in Barrow, Cumbria, in 2012.
She died in June after her family fought for a legal ruling to withhold nutrition and hydration.
The coroner ruled she died of a brain injury resulting from the overdose.
Ms Simpson's brother Michael Devlin told the inquest his sister had a history of drink and drug use and had been on a "weekend bender" before he found her collapsed at her home.
She ended up in a vegetative state with no sign of consciousness.
She was able to breathe without assistance but needed to be fed and given liquid through a stomach tube.
Her mother Jean Simpson said: "I knew from the beginning there was no hope, my worst fear was that she was actually minimally unconscious.
"No one would want to live like that."
Doctors agreed there was no chance of recovery yet the legal application to allow her to die was subjected to years of delay.
She told the inquest her family was "treated as insignificant" by the authorities and she had lost faith in professionals.
Cumbria Care Commissioning Group has since apologised for the process taking so long.
The coroner said looking back to the events of 2012, there was no evidence Jodie Simpson intended to take her own life.
Sainsbury's has said sales of clothes, summer food and paddling pools helped speed up growth in the past few months.
[NEXT_CONCEPT]
A woman who spent four years trying to get permission to allow her daughter to die has told an inquest the delay was "excruciating".