Sales for the Europe-wide business rose 14% in the 16 weeks to January 4, driven by an 8% increase in selling space and more strong growth at stores which have been trading for more than year.
In contrast to the performances of Primark and rival Next, which has already posted a surge in sales, M&S's general merchandise sales were down 2.1% for the 13 weeks to December 28. Its boss, Marc Bolland, blamed a vicious Christmas price war for the decline.
Primark, which has 161 of its 257 stores in the UK, is on course for further profits growth this year, on top of the 44% jump in profits to £514 million recently announced for the year to September.
Its owner, Associated British Foods, said that like-for-like growth already achieved and further store expansion meant Primark's profit "will be well ahead of last year".
AB Foods, which also owns leading food brands Ryvita, Twinings and Kingsmill, said Primark's strong performance offset a 28% fall in revenues at its sugar business due to a slump in global prices.
Sales volumes at Kingsmill owner Allied Bakeries were higher despite strong competition, while Twinings Ovaltine saw strong growth for tea in the UK and United States.
Anusha Couttigane, an analyst at retail consultancy Conlumino, said: "Primark remains the jewel in the crown for Associated British Foods.
"Primark is no longer the only retailer to offer fast, seriously cheap, fashion. However, the company's sustained reaction to fast fashion means it is still the number one destination for many buying into temporary trends on a budget.
"It is, therefore, unsurprising that this Christmas established Primark as the prime destination for onesies, capitalising on a key winterwear trend."