Tesco's overall sales fell by 0.8%, halving last period's decline of 1.6%, after a renewed focus on price promotions helped stem the flow of shoppers leaving the retailer, according to Kantar Worldpanel.
Tesco's positive run follows it closing around 50 stores in the last year.
The figures for the 12 weeks to the end of February show a small increase in supermarket sales which are up by 0.5% compared with a year ago - the fastest rate of growth since October 2015 but restrained by the continuing fierce price war and grocery prices down 1.6%.
Sainsbury's was once again the only one of the big four to boost sales, seeing growth for the eighth quarter period in a row, up by 0.5% but leaving its overall market share flat at 16.8%.
Morrisons' cutting of stores since last year contributed to its sales falling by 3.2% and a dip in its market share to 10.6%.
However, its online sales grew strongly, and the report predicts its forthcoming tie-up with Amazon could provide "another boost to the business".
Sales in larger stores across the market fell by 2% as consumers spent less per average trip in these shops, disproportionally affecting Asda, whose sales fell by 4% and market share dropped to 16.2%.
Waitrose saw its sales grow by 0.2%, maintaining its 5.2% share of the market for the third period in a row.
The Co-operative increased its market share to 6% after an increase in shopper frequency contributed to a sales increase of 1.9%, while discounters Aldi and Lidl saw their share climb back to the 10% high they reached before Christmas.
Lidl's sales grew by 18.9% and Aldi's by 15.1%.
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