The supermarket chain said like-for-like sales, excluding fuel, rose 0.2% in the nine weeks to 3 January.
Analysts had expected a fall in sales at Morrisons, which has been under intense pressure from rivals.
It is the first time the supermarket has reported a rise in sales for more than a year.
The results sent shares in Morrisons up sharply, and they closed more than 8% higher at 165.5p.
Paul Thomas, an analyst at Retail Remedy, said Morrisons' sales had been expected to fall by between 2% and 3%.
He said the UK's fourth-largest supermarket chain was clearly focusing on "its core market and core product" and that the sales figures were evidence that the new strategy was "paying off".
David Potts, who became chief executive of Morrisons in March last year, said he was pleased with the performance over Christmas: "While there is of course much more to do, we are making important progress in improving all aspects of the shopping trip."
He sold its 140 M Convenience stores at a loss of £30m in September and has also embarked on a cost-cutting and store closure programme.
Last year, Morrisons reported a 52% drop in annual profits to £345m - its worst results in eight years.
The retailer also dropped out of the FTSE 100 list of the UK's biggest companies in December.
The increase in sales came as Morrisons continued to cut prices -  by 3.2% in the last year and 7% over two years.
It said customers were also returning, with transactions up 1.3% in the period.
However, total sales were down 1.2%, which Mr Thomas said suggested that customers were buying fewer items.
Morrisons maintained its profit forecast, saying it expected full year underlying profit in the region of £295m to £310m, before £60m of restructuring and store closure costs.
According to new figures from research firm Kantar Worldpanel, Morrisons' share of the overall grocery market was 11% in the 12 weeks to 3 January, down from 11.3% a year earlier.
Sainsbury's was the best performing of the "big four" supermarkets - which includes Tesco, Sainsbury's Asda and Morrisons. Its market share rose 0.1 percentage points to 17% compared with the same period in 2014, making it the only one of the big four to increase its share.
Discount chains Aldi and Lidl, as well as the Co-operative and Waitrose, were the other chains to increase their market share in the 12-week period.
Tesco kept the number one slot, with a 28.3% share, although this was down from 29.1% a year earlier.
Overall, the value of sales in the 12-week period was down 0.2% due to continued price deflation,  Kantar said.
Analysts reacted to Morrisons' sales figures with surprise, with Nick Bubb tweeting: "Wow Morrisons was actually up 0.2% LFL at Xmas".
Morrisons is the first of the "big four" to release Christmas sales figures, with Sainsbury's publishes its third-quarter results on Wednesday, followed by Tesco on Thursday.
Walmart-owned Asda does not release its figures until February, but it has predicted another year of "intense pressure".
Last week, M&S said third-quarter sales of general merchandise were down by 5.8% for the 13 weeks to 26 December, although food sales were up 0.4%.
It also said chief executive Marc Bolland would step down in April, to be succeeded by Steve Rowe, head of general merchandise.
Like-for-like sales at Waitrose, the  supermarket owned by the John Lewis Partnership, fell 1.4% over the Christmas period, although John Lewis sales overall rose 5.1%.
Morrisons has reported better-than-expected sales over the Christmas shopping period compared with a year earlier.