As Yahoo plots a new course under CEO Marissa Mayer, it may want to study what's happened with eBay in recent years. After a long and dicey effort, the online retailer has pulled off a rarity in the Internet industry: It turned around a business that many critics has written off as dying. Here's how a combination of bold product redesign and mobile innovation did the trick.

eBay used to be among the Internet's walking wounded. The company's stock, having soared to $59 a share in 2004, fell to $26 in early 2008, when CEO John Donahoe replaced Meg Whitman. Since then, Donahoe has pursued a turnaround of eBay's marketplace business that involved shifting from auctions to fixed-price sales and focusing on top sellers, even at the cost of marginalizing many smaller sellers.

At first, the turnaround seemed not to be working. One year into Donahoe's tenure, the stock price had slipped below $10 and Donahoe was on the defensive with disenchanted investors. But he stuck to his guns. After all, turning around a business can take years, even on the Web. And four years of effort to revive eBay's marketplace, signs of success began to emerge.

Now it's like the company has awakened from a bad dream. As of Friday, eBay's stock is up 55% this year, three times the Nasdaq's 18% rise and better than Amazon's 39% gain. The stock at its highest since January 2006, pushing its market cap above $60 billion. By contrast, Facebook's market cap is $46 billion (or $52 billion, using a more generous calculation).

That comparison is significant. In a little more than three years, eBay has managed to grow from a company worth $16 billion to one worth $60 billion – and it did so in the Web 2.0 era, one that was dominated by younger companies like Facebook and Zynga. While those companies face their challenges, eBay has overcome its own. And it's doing so in the same arena where Facebook is stumbling: the mobile Web.

eBay is forecasting that $10 billion worth of transactions will happen through mobile phones this year, double the figure last year. That's equal to one sixth of the $60 billion in gross merchandise value eBay reported in 2011. In a recent call with analysts, Donahoe, noting that mobile shoppers spend three to four times as much as people who shop only on the Web, called that growth “a stunning surge in purchases and payments on devices that did not even exist just a few short years ago.”

PayPal, which has seen a similar surge in mobile payments, is also expected to handle $10 billion in mobile transactions this year. But the recovery in eBay's core marketplace business is all the more impressive given that its growth rates had stalled in recent years.

eBay's marketplace generated 15% growth in the most recent quarter, excluding the impact of foreign-exchange rates, the fastest growth since 2006. The bulk of that growth is coming from the fixed-price items that Donahoe redesigned eBay's site around several years ago. After sluggish growth in 2009 and 2010, eBay drew criticism for abandoning the auction model that made the company a success to begin with, and for adopting too late a model that closely resembled one long used, with great success, by Amazon.

But in the second quarter, fixed-price sales accounted for two thirds of the company's transactions, up from 53% in 2009. Fixed-price sales grew 20% in the quarter, compared with a 4% growth rate for auctions.

eBay also saw early on an opportunity in mobile and designed an app that appealed to mobile shoppers with features like one-click shopping, offering it an early lead that it still holds. The company bought Critical Path Software, whose developers helped design a simple yet intuitive eBay app.

Of the 45 million people who used a shopping app on a smartphone in June, 13.2 million used eBay's, placing it ahead of Amazon (12.1 million) and Groupon (12 million). And people spent much more time on eBay's app, 64 minutes on average, compared with 19 minutes for Amazon and 21 minutes for Groupon.

eBay continues to improve its marketplace, tweaking the design and search to improve the user experience and building online storefronts for big retailers like Toys “R” Us, Aeropostale and Nieman Marcus. And the company announced a plan to offer same-day delivery in San Francisco, working again with top retailers like Macy's and Target.

The years of rapid growth are behind it, but eBay is showing that its future is more than a one-time auction giant that is morphing into an e-payments outfit. The company is proving that, in the age of the mobile Web, it can find a new role for itself in e-commerce. Turnarounds like that are as rare as gold in the Internet industry.