The stock gained 9.8p, or 14.8%, to 75.8p as Debenhams said like-for-like sales rose 3.5% in constant currencies and by 1.9% on a reported basis in the 19 weeks to January 9.
In the seven weeks to January 9, like-for-like sales gained 3.7% while online sales rose 15.4%.
Less discounting and fewer promotions led to full-price sales growth of 5%.
Internationally, Debenhams performed in line with expectations, with its Magasin du Nord chain in Denmark delivering a record Christmas.
Debenhams said a planned reduction in outerwear clothing stocks helped it to trade a difficult autumn clothing season successfully and it went into the post-Christmas sales with less stock than a year ago.
Non-clothing categories now make up 55% of total revenues, with sales of beauty products increasing strongly.
Outgoing chief executive Michael Sharp said: "We have traded well in the first 19 weeks of the financial year with a strong performance over peak resulting in a record Christmas. We remain on track to deliver full year profits in line with market expectations."
Hargreaves Lansdown analyst Keith Bowman said the performance contrasted favourably with that of Marks & Spencer (LON:MKS) and Next (LON:NXT), although the middle ground Debenhams occupied between discount and high end clothing retailers remains challenging.
He said: "In all and despite current success, Debenhams remains in transformation. Consistent progress will be required in order to fully convince, with analyst consensus opinion, at least for now, pointing towards a weak hold."