The department store chain reported a 1.9% rise in like-for-like sales for the 19 weeks to 9 January, with growth of 1.8% in the final seven weeks.
It hailed a successful Black Friday and record performance in the Christmas week, adding that it continued to rein-in promotions despite widespread discounting on the high street in December after unseasonably warm weather, with full-price sales up 5%.
Debenhams, which has around 160 UK stores out of more than 250 worldwide, said it cut back on certain clothing lines such as winter coats to overcome the impact of the warmest December in over 100 years.
Rivals such as Next and Marks & Spencer were hit as shoppers shunned heavy coats in favour of lighter-weight items in November and December.
Shares in Debenhams raced more than 14% higher on the better-than-expected festive performance.
Outgoing chief executive Michael Sharp, who announced plans last October to leave in 2016, said the sales rise shows turnaround efforts are continuing to pay off.
He said: "This performance is evidence that our strategy is working."
The update comes after Debenhams posted its first rise in annual profits for four years in October, when underlying pre-tax profits rose 2.9% to £113.5m.
Retail experts praised the group's Christmas trading.
Keith Bowman, equity analyst at Hargreaves Lansdown Stockbrokers, added: "The update offers firm reassurance.
"A planned reduction in outerwear clothing stocks has clearly played its part, while management's push to increase online sales continues to progress.
"A focus on non-clothing categories is also reaping rewards, with new store opening further contributing."
Debenhams, which also trades as Magasin du Nord in Denmark, said online sales lifted 12.1% over the 19 weeks and 15.4% in the key seven-week period.
On a constant currency basis, like-for-like sales rose 3.5% over the 19 weeks.
In October, Debenhams revealed Sharp will stand down at some stage in 2016 after nearly five years at the helm.
The announcement came amid reports that some of the company's major investors were unhappy with its performance, and were seeking a board shake-up after disappointing results in previous years.
But the latest trading update suggests its recovery is on track and earns the chain a place on the list of retail Christmas winners so far.
It also puts competitors Next and M&S in the shade, with both seeing store clothing sales fall over the Christmas season due to stock woes amid the mild weather.
Next reported a 0.5% fall in store sales in the 60 days to December 24 and a slowdown in sales growth its Directory and online arm, while M&S suffered a 5.8% drop in like-for-like sales in its general merchandise arm, which includes womenswear.
Debenhams was helped as it boosted its non-clothing sales, now accounting for more than 55% of group sales thanks to strong demand for ranges such as beauty, gifts and electricals.
It sold nine million seasonal gifts over the period, with "must-have" gadgets including drones, with more than 25,000 sold.
Sharp said: "We have enjoyed a record Christmas trading period including our best ever December and Christmas week.
"We are particularly pleased with our performance in beauty and gifts where we delivered a good result in store along with strong online sales."
The group saw online sales in the Christmas week jump by 36%, while internet orders rose by a fifth on Black Friday, peaking at 220 orders a minute.
Debenhams added that the Black Friday one-day promotion in late November saw sales more than quadruple in stores.