When Walmart's stock plunged 10% in a day last month after warning its earnings next fiscal year will fall, much of the blame went to investments to fix up old supercenters and wage increases for workers. But what also played a role was a $1.1 billion investment in e-commerce, largely to compete against Amazon.

Even so, Walmart expects net income of more than $13 billion next year. By comparison, Amazon has posted profits the past two quarters totaling $171 million, mainly driven by a lucrative cloud computing business.

More than two decades into its e-commerce business, Amazon still doesn't reliably post profits from it, plowing almost everything back into growth. And Wall Street loves it, more than doubling Amazon's stock price the past year and giving it a price/equity ratio of more than 800. By contrast, Walmart's stock is down 26% the past year, with a P/E ratio under 12. Amazon has less than a quarter of Walmart's nearly $500 billion annual sales, but its market capitalization is more than $100 billion higher.

So how can Walmart compete with Amazon in e-commerce when the latter doesn't really make money at it? "It's a huge question," said Bernstein Research analyst Ali Dibadj, who said he posed it to Walmart CEO Doug McMillon following the retailer's investor presentations last month. The answer he got was that Mr. McMillon feels the market will eventually force Amazon to be more profitable. Mr. Dibadj said he isn't so sure.

Walmart's e-commerce sales have slowed from north of 30% two years ago to a projection of a "mid-teens" percentage increase this year. Its $12 billion in e-commerce sales last year pales next to Amazon's $85 billion-plus, though Amazon, which declined to comment, has seen a similar slowing in e-commerce driven by weakness in overseas markets.

Simultaneously, Walmart faces plenty of brick-and-mortar competition from the likes of Costco, Aldi, Trader Joe's and Dollar General-which have been beating it in top-line growth for years while placing far less emphasis on e-commerce. So wouldn't Walmart be better off letting others take on Amazon in an e-commerce business while it focuses squarely on its stores?

The answer is probably no, at least not in the long term.

Consider signs Walmart is winning with millennials, which could help it avert the declines of such other once-dominant retailers as Sears, Kmart and A&P.

Compared with rivals overall, Walmart fares better in terms of share of wallet with millennials. The mega-retailer nets 23.8% of millennials' spending vs. the 22.3% from U.S. shoppers overall, according to data from InfoScout, which collects data from grocery and consumables receipts scanned by its shopper panelists. Other key competitors that over-index with millennials in InfoScout spending data, such as Target and CVS, have similarly focused on e-commerce. But Costco, Aldi, Dollar General, Trader Joe's and Kroger, all of which have been outgrowing Walmart offline, have focused less on their e-commerce operations, and all under-index with millennials today.

So Walmart's e-commerce push, which had made it No. 3 behind Amazon and eBay, may well pay off long-term. But it's a very long game. Millennials represent around $200 billion of U.S. buying power today, but consumers 50 and older, who over-index with many of Walmart's rivals, represent $3.2 trillion. "Walmart has its eye on the long-term right now," said spokesman Dan Toporek. "We believe that's the most critical way to look at investment."

Mr. McMillon noted in his October presentation that Walmart's average online-only customer spends only $200 a year with the retailer. Its average store-only customer spends $1,400. But customers who buy "omnichannel" with Walmart spend more than $2,500 with the retailer annually.

"These are the customers everyone is chasing, and we already have a relationship with so many of them," he said. "This overlap will continue to grow. Eventually, it will be our biggest revenue segment."

But for now, competing against Amazon means taking losses. Though Walmart projects narrowing (if unspecified) losses on e-commerce through fiscal 2019, it's not yet projecting when e-commerce profitability will arrive.

Walmart is also testing Shipping Pass-an Amazon Prime-like program for unlimited free shipping-which could mean an even bigger pool of red ink. Mimicking Amazon with free shipping "isn't sustainable in the long run and will cost retailers billions," said Jeremy Bodenhamer, CEO of ShipHawk, a logistics automation company. One path Walmart is trying is grocery pickup in such markets as Denver, Northwest Arkansas and Huntsville, Ala. Mr. McMillon says it has the "potential to bring in meaningful amounts of new customers." In the past six months, one in four grocery pickup customers in Denver is new to Walmart.

"It is a key differentiator for us that customers can eventually pick up a snow shovel in the winter with their milk and eggs without getting out of the car," he said.

Walmart has gone from five such pickup locations nationwide to 23 in the past year. It will add another 20 such grocery pickups, which resemble Sonic restaurant drive-up stations in many places, in the fiscal first quarter that ends next April, Mr. Toporek said, "and then each quarter we'll continue to build on that."

Walmart also appears to be taking a swipe at Amazon's cloud profitability. Walmart CEO Global E-Commerce Neil Ashe at last month's investor conference announced plans to make its OneOps technology, which makes it easier for companies to move data and software from cloud to cloud, available to others for free. That should "create competition" and "lower the cost of cloud services for all of us," Mr. Ashe said, not to mention potentially take a chunk out of Amazon's most profitable business.

"We never said anything about going after Amazon, but people kind of jumped on that," Mr. Toporek said. Walmart operates its own private cloud, he said, but OneOps allows it to use other cloud proviers to handle peak demand during holidays, and it wants to make that flexibility available widely.

The cloud business aside, Consumer Edge Research analyst Stacie Rabinowitz sees signs that Walmart can compete with Amazon. A Consumer Edge study earlier this year found Amazon prices on consumables tend to be much higher than those at Walmart or Target-before figuring in the value of free-shipping options. And online shoppers for Walmart (and Target) tend to shop their sites more frequently than Amazon shoppers do, in part because of emphasis on consumables over durable items, creating more cross-selling opportunities. Walmart also gets high marks for product selection from shoppers.

"The more Walmart does to differentiate itself from Amazon and offer a better value proposition, the more it will succeed," she said. "The more it focuses on price and value, the more it can compete."

Investing in things like drone delivery, she said, isn't likely to help, but strategies that use e-commerce to help bring people into stores to buy or return items have more promise. "There's still a big percentage of the population that doesn't have a credit card to buy things online," she said, "and being able to pay cash in stores is a big advantage."

With Walmart already largely beating Amazon on price, she said, Amazon may also face growing pressure to be profitable, making it harder to cut prices or sustain generous free-shipping policies. "At some point, the markets are going to make Amazon show more profitability," she said, and the fact that Amazon already has posted modest profit the past two quarters suggests it sees that need, too.