The UK's second biggest supermarket chain has been trying to regain ground after shoppers turned to cheaper rivals as the cost of living has soared.
It said customers who used to shop only at the discounters were now buying items in Sainsbury's too.
Grocery sales at Sainsbury's were up 10% in the six months to 16 September, compared with a year earlier.
Sainsbury's said the sales hike was driven not just by price rises, but by the fact that shoppers were also buying more items.
However, the supermarket's profit before tax dropped by 27% to Â£275m.
Clothing sales, in particular, were hit by a cooler summer and warm early autumn, reducing demand for seasonal items, the company said.
Household budgets have been hit hard by inflation, the rate at which prices rises.
As cost of living pressures squeeze shoppers, they have been turning to Aldi and Lidl as they hunt for bargains.
Both supermarket chains have been opening stores as they battle for shoppers with the more established players in the UK: Tesco, Sainsbury's, Asda and Morrisons.
Sainsbury's said it had not gained more of an overall share of the market, but it did claim that it was the only big supermarket to be winning back customers and gaining spend from Aldi and Lidl.
Its chief executive Simon Roberts said: "We know people are still finding things tough and we're working harder than ever to reduce our costs, putting the money back into our customers' pockets through lower prices on the products they buy most often."
He added: "Food inflation is coming down and we are passing savings on to customers."
Sainsbury's has been running an "Aldi price match" campaign as part of its battle.
However, Aldi said: "Shoppers know that the only place to get Aldi prices is at Aldi.
"That's why we've been confirmed as the UK's cheapest supermarket for 16 consecutive months, growing our market share and attracting around one million new customers."
Lidl said it did not comment on competitor activity.
Earlier this year, supermarkets were investigated by the Competition and Markets Authority after concerns that customers were overpaying for food and fuel.
The watchdog found that higher food costs had not been passed on in full to consumers and that people were shopping around to get the best deals.
But it said that customers had been overpaying for fuel.
Mr Roberts said on Thursday that the group's food price inflation was running at half the level reported by the Office for National Statistics (ONS), with price cuts in some areas such as fresh food.
The ONS said in Octoberthat food price inflation remained high at 12.2% on an annual basis, but had been easing.
Sainsbury's has said customers are starting to switch back from discounters Aldi and Lidl.