Prices on a range of products including coffee and laundry liquid went up by as much as 60p at the store in Hampshire Centre mall.
Yesterday a senior company representative visited Bournemouth to apologise to the shoppers, and return prices to their original level, as the issue was featured on Radio 4's consumer programme You and Yours.
One shopper, Marilyn Rigler had spotted two weeks ago that jars of Nescafe coffee had soared by 19p from pounds 1.79 to pounds 1.98. Checking the price against identical jars in another Sainsbury's just three miles away in Boscombe, she was amazed to find that the rise applied only to her store.
Mrs Rigler said: "A friend of mine mentioned that sherry had gone up by about 50p a bottle, so I made lists of items in the two stores, and found that there was a whole range of them that were more expensive at the Hampshire Centre.
"There didn't seem to be any logic to which ones were chosen. There were own-brand products and big brand-names like Kellogg's, and the rises ranged from 4p to 60p."
She added: "I think it's sneaky. If they put a few pence on their prices a lot of people probably don't notice while they are filling their baskets, but it all adds up. Most people are watching their budgets nowadays and they can't afford to pay more for their food. Who knows how long its been going on?"
The chain - which announced a 15 per cent slump in pre-tax profits in its annual results on Wednesday - said that the variations in price were part of market research which was "limited to a small number of stores and a specific time frame".
A spokeswoman said that the increased prices had been scheduled to be phased out over the next few weeks, as the project ended.
She added: "We carry out constant research into many elements of our offer, and monitoring our prices against competition is part of it.
"Market research is an ongoing process for any big company. We are looking at the relationship between price, service, quality and in-store facilities."
But Mrs Rigler was not impressed: "They talk about customer loyalty, but customers will only be loyal to a shop as long as the shop is loyal to them."
A spokeswoman for the National Consumer Council said: "Maybe Sainsbury's are testing whether we consumers are awake as we fill our trolleys.
"The message to consumers has got to be the traditional advice - stay alert and shop around.
"You cannot assume that supermarkets will give you the best deal or that they will charge the same wherever you are in the country. This case proves that."
Similar experiments had been carried out in other industries, she said, but this was the first time she was aware of it being done by a supermarket.
A spokeswoman for the National Consumer Council said: "The message to consumers has got to be the traditional advice - stay alert and shop around. You cannot assume that supermarkets will give you the best deal or that they will charge the same wherever you are."