The high street fashion chain's growth helped drive revenues up at owner Associated British Foods (ABF), which saw group revenues rise 4% over the 16-week period to January 4.
Primark saw its UK sales grow by 4% as it benefited from new stores and expansions, while sales across the retailer were up 3%.
The company hailed "good trading" over November and December, despite highlighting a "marginal decline" in like-for-like sales.
Primark said it heavily benefited from three store openings during the period, as well as site expansions.
It said it expects to open 18 new stores during the financial year as it continues its expansion programme.
John Bason, chief finance officer at ABF, said the retailer performed well given "softer volumes" across the retail market.
He told the PA news agency: "The UK consumer has more discretionary income than before but spending has decreased so there is clearly a degree of caution in retail and there has been in other areas.
"I think Primark has made a clear statement here and I think we performed well because we went back to basics.
"There were great products which had a clear relevancy with the consumer and that is what worked for us in November and December."
Elsewhere, ABF was bolstered by its strengthening sugar business, which saw revenues increase 5% after EU sugar prices remained higher than over the same period last year.
It said lower costs in sugar production also mean that there will be a material improvement in profits from the sugar arm, particularly in the second half.
ABF said grocery sales were level against the same period last year, although profit margins improved.
Increased popularity of herbal teas in the UK and US helped to improve revenues at its Twinings division, while efficiencies in the tea supply chain also helped to improve profits.
ABF said operating losses at its troubled Allied Bakeries business, which makes Kingsmill bread, were reduced after "progress from cost reduction" more than offset lower sales.
Sophie Lund-Yates, equity analyst at Hargreaves Lansdown, said: "What's most striking about Primark is it's essentially an old school retailer. Lack of a meaningful online business makes the chain a high street play, so the improvement to sales performance is even more impressive.
"Within the UK, repeat business did dip slightly, but new store space is offsetting that - which has been the tactic for a while now."
Shares in ABF increased by 2.8% to 2,626p in early trading.