Uber (UBER -2.50%) has fully recovered from the COVID-19 pandemic. However, the same cannot be said of its chief rival, Lyft. The two ride-sharing companies reported drastically different sets of third-quarter results earlier this month. The trend shows Uber is taking market share from its smaller rival.

There's one key advantage that is giving Uber the ability to grow its ridership faster than Lyft, and that advantage could also help it take on competitors in the delivery space, among others.

Uber's app is becoming the only one you need

In 2019, Uber decided to integrate Uber Eats, its food delivery service, into its main ride-sharing app. That move telegraphed much about the company's longer-term strategy.

Uber has since expanded its services to include grocery and alcohol delivery with the help of some tuck-in acquisitions. It's also expanding its services so that users can make restaurant reservations or buy event tickets through its app. For nearly anything that involves you leaving your house or having something delivered to it, Uber eventually wants you to be able to use its app.

It has been able to build out its services because of its vast networks of drivers and riders. That user base helps it attract restaurants and stores to its delivery platform, all of which drive a virtuous cycle through which it can offer more services to consumers, provide more opportunities for drivers, and grow its overall network.

That's a big competitive advantage over Lyft and other gig economy companies like DoorDash.

The efforts are paying off

The benefits Uber accrues by offering multiple services are already paying off in the form of greater user additions, engagement, and retention.

"We are actively cross-selling ... food delivery consumers into grocery, grocery consumers into alcohol and then actually back now to mobility as well," CEO Dara Khosrowshahi said on Uber's third-quarter earnings call.

While the mobility business initially supported the growth in the number of delivery users, the trend is now reversing. During the earlier stages of the pandemic, millions of new users signed up for food delivery services like Uber Eats. Today, Uber is able to take advantage of that massive user base to help its mobility business recover.

"[W]e are now offering mobility promos, for example, to ... [delivery] users who either have churn[ed] or mobility [to] users who've never used mobility before," Khosrowshahi said. "And we're seeing really great promise in terms of delivery actually being able to cross-promote and drive mobility use cases."

Indeed, the numbers of both active Uber riders and drivers have recovered to 2019 levels, according to management. Meanwhile, Lyft's ridership remains more than 10% below its 2019 peak.

Can Uber dominate both markets?

Uber already dominates the ride-share industry, but it's solidly in second place when it comes to its delivery business. Its delivery gross bookings grew by just 13% last quarter. Meanwhile, DoorDash's gross order value grew by 30% year over year, including a 10 percentage point contribution from its acquisition of Wolt. Even looking exclusively at DoorDash's organic growth, Uber is losing ground.

But investors shouldn't fret. The same advantage that allowed Uber to rebuild its mobility business ought to lead it to eventually take back market share in the delivery niche. Even as DoorDash exclusively invests in expanding its delivery service, Uber is capable of keeping up.

Uber's delivery business just became profitable on an adjusted EBITDA basis. That, in combination with its recovering mobility business, has the company starting to generate significant free cash flow. This will allow it to invest in building out its services and compete on delivery with DoorDash, which in turn will give it more cross-selling opportunities to grow and engage its customer base.

I expect Uber to grow its share of the delivery market over the long run as it benefits from its massive network of consumers and drivers. After all, these enable it to expand quickly, attract new users, and grow profitably.