Data from Kantar Worldpanel also showed price rises were accelerating as they continued to pick up after more than two years in decline.
The figures showed the total grocery market grew by 3.7% to £26.4bn in the 12 weeks to 23 April, the fastest rate since September 2013.
All 10 major retailers saw growth, the first time this has happened in three-and-a-half years.
That was despite fears over a squeeze on household budgets as inflation accelerates and wage growth stalls.
Easter was a major contributor, with £325m spent on Easter eggs while 20 million packs of hot cross buns were sold in one week alone.
Three quarters of the population bought at least one egg with premium brands proving popular - taking the average price up by 8.6% to £1.65.
Prices in the grocery sector were climbing at an annual rate of 2.6%, also the strongest pace for three and a half years, following 30 months of decline up to the end of 2016.
But Kantar said this rate was still below the average level of grocery inflation experienced between 2010 and 2014.
Sainsbury's sales growth of 1.7% was its strongest since June 2014 - though the figure came on the same day as Britain's second biggest supermarket reported a fall in profits and warned of continuing challenges amid tough competition.
Asda posted its first increase for more than two years while Tesco and Morrisons also saw growth.
However, all of the big four supermarkets still saw their market share decline compare with last year as discounters Aldi and Lidl posted more double digit growth.
Separate industry figures compiled by Nielsen also showed strong growth, with sales up 3.2% in the eight weeks to 22 April.
Mike Watkins, Nielsen's UK head of retailer and business insight, said it counterbalanced "rather downbeat" stories about wider consumer spending, squeezed by rising inflation and stuttering pay growth.
Separate data from the British Retail Consortium (BRC) showed that across the wider sector, including fashion and homeware as well as food, prices were still falling.
However, deflation of 0.5% in April compared to a larger price fall of 0.8% in March.
BRC chief executive Helen Dickinson said: "Prices are undoubtedly on an upward trajectory, which we expect to gradually play out over the course of the year."