Sales at the UK's biggest supermarket increased by 2.2% over the quarter to November 6, ahead of overall sales which increased by 0.8% year-on-year for the second consecutive month, according to Kantar Worldpanel.
The discounters grew at their slowest rate since 2011, however Aldi still increased its sales by 10.2% with 547,000 more shoppers visiting over the 12 weeks - a bigger increase in visitor numbers than any other retailer - and Lidl's sales were up 6.1%.
Iceland's sales grew well ahead of the market at 8.3%, increasing its market share to 2.1%, as a high-profile store opening in Clapham, London "clearly targeted at millennials" supported its increasingly upmarket range.
Sales at Sainsbury's declined by 0.7%, while Asda's decline slowed slightly to 5% and Morrisons saw total sales fall by 2.4% in line with its smaller number of stores.
Fraser McKevitt, head of retail and consumer insight at Kantar Worldpanel, said: "Tesco's 2.2% growth is a considerable improvement on the numbers it was delivering this time last year, and indeed in 2014.
"Much of Tesco's growth has come from more affluent shoppers returning to the store, and average spend per trip is up by 2.1% to £20.69."
The figures also show that grocery prices have now been falling continuously since September 2014 and are still 0.5% cheaper than last year, although this is a significant reduction in the rate of deflation since this summer.
McKevitt said: "We're likely to see prices starting to creep up again in December, unless retailers choose Christmas to unleash a new round of price cuts.
"Although it's tempting to link any potential price increases to Brexit and the devaluation of sterling, it's worth remembering that deflation has been easing since December last year, well before the referendum."
Figures from analysts Nielsen also show sales growth at both Aldi and Lidl hit the lowest level in five years, increasing by 11.3% and 5.2% respectively.
Between them, Aldi and Lidl account for 11.8% of UK grocery sales, up from 11.1% a year ago.
Mike Watkins, Nielsen's UK head of retailer and business insight, said it was "inevitable" that the discounters would eventually experience a slowing growth rate, noting that Tesco's 2.3% growth continued apace.
He said shoppers were continuing to spend freely "despite the so-called Brexit impact, which in reality isn't expected to 'hit' consumer spending until next year".