CNBC-  Krystina Gustafson | @KrystinaGustafs 

Luxury retailers are having another rough year, as value-conscious consumers balk at the idea of shelling out big bucks for the latest designer goods. Yet as the high-end market struggles to eke out revenue growth, there's one area where sales are flourishing: The web.

Following years of arguments that shoppers would not be willing to purchase a $4,000 handbag online, research published by Walker Sands Thursday has found that 27 percent of consumers purchased a luxury item on the web in the past year. That's up 17 percentage points from just last year, and represents a 21-point gain over 2014.

The trend is skewed toward millennial shoppers between the ages of 18 and 25, though older shoppers are also adopting the habit. According to Walker Sands, one-third of millennials bought a luxury item online over the past year, compared with 6 percent for those ages 61 and older.

The digital marketing agency said its findings, which were based on an online survey of more than 1,400 U.S. consumers, line up with industry predictions that digital luxury goods sales will triple to around $80 billion by 2025.

The report also comes as several recent studies have disagreed over whether online sales are positioned for a second wave of growth or are about to plateau.

"While luxury commerce has had a slow start in the online space, more than four times as many consumers made luxury purchases online in the past year compared to two years ago," Walker Sands' report said. "With estimates that online sales could make up to 40 percent of luxury sales by 2020, the luxury industry is seeing much larger growth than many other areas of e-commerce."

Much of luxury retail's online growth can be pegged to an increase in spending at Amazon or other third-party retail sites. According to Walker Sands, 22 percent of shoppers said they purchased a luxury good on one of those players over the past year, up from 5 percent in 2015. That compares to 10 percent of shoppers making a purchase on a brand's website, up just 3 points from last year.

Some of this discrepancy can be explained by the fact that many luxury retailers were late to the game — for example, shoppers still can't make purchases through Chanel's official website. Yet Amazon has also zeroed in on fashion as an opportunity for growth.

"One of the biggest drivers of online luxury sales for third-party websites likely has to do with the general rise of Amazon and the comfort of consumers spending large amounts of money online — which also increases with free shipping," Walker Sands' Erin Jordan, who worked on the report, told CNBC.

According to the firm's research, 98 percent of people reported having made a purchase on Amazon in the past year. Yet Jordan said there are opportunities for brands to catch up, as more shoppers said they are open to making a luxury purchase on a label's own website than through Amazon or another third party.

Luxury retailers also stand to gain by adopting virtual reality, as more luxury buyers said they're more interested in using the technology for online shopping than the average consumer, Walker Sands said.

Even as more shoppers head to the web for luxury goods, the majority of sales still take place in stores. According to Walker Sands, the majority of shoppers prefer to make purchases at physical stores in every category except books, consumer electronics and office supplies and grocery.

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