The company's UK arm experienced a 24% lift in sales for the quarter to £104m, up from £84m over the same period last year.
But CEO Nick Robertson admitted the global picture was still "challenging", with international sales for the quarter down 2% to £142m.
Outside the UK, Europe and US, international sales fell 6% to £59m. Total group revenues were up 8% year on year to £252m.
Asos has issued multiple profit warnings over the past year, driven by a fire at its Barnsley warehouse and the difficult launch of its business in China in 2013.
Robertson said Asos had now received insurance for the Barnsley fire which would help keep full-year profits in line with expectations.
He said: "September and October were challenging as we completed the automation programme in Barnsley in time for peak.
"Our sales have since gathered momentum and we had our biggest ever trading week over cyber weekend in November."
Finspreads analyst Fiona Cincotta noted, however, that fundamental flaws in Asos' business model meant the firm's troubles were unlikely to be over.
She said: "Asos continues to suffer from what is starting to look like an structural (almost built-in) problem with its business model of mid-tier-to-low-price online fashion.
The central issue is of course, that Asos is in ultra-competitive segment with relatively low barriers to entry.
"The main battle grounds are the realms of margins – also known to the lucky consumer as ‘price cuts’ – marketing [which] requires a highly engaging and constantly evolving online content strategy, operational nimbleness and reactiveness."