On Tuesday, Amazon blinked and Roxbury gained a small measure of economic respect.

The online retailing giant abruptly changed course and announced it will soon offer same-day “Prime’’ delivery to residents of Roxbury, the only neighborhood in the Boston area excluded from the service.

“We are actively working with our local carrier to enable service to the Roxbury neighborhood in the coming weeks,’’ an Amazon spokesman said in a statement. “Once completed, Prime members in every ZIP code in Boston, including the Roxbury neighborhood, will receive Prime Free Same-Day Delivery.’’

Amazon had been facing a gathering hurricane of public outrage and political pressure since an analysis published last week by Bloomberg showed Amazon does not provide same-day delivery in just three ZIP codes in Boston, all in Roxbury. The neighborhood is encircled by areas that receive same-day deliveries, prompting residents and politicians to denounce Amazon’s “doughnut-hole’’ map as unfair and discriminatory — not to mention logistically nonsensical.

On Tuesday, community leaders praised Amazon’s reversal, saying it was an important and highly visible win in a broader fight for economic equality among the city’s neighborhoods. But they remain upset and puzzled that the company carved out predominantly black Roxbury from its delivery zone in the first place, especially since Amazon and other hot tech firms in the “on-demand’’ space are already under fire for a lack of diversity in their workforces.

“I commend [Amazon] for fixing it,’’ said Damon Cox, a director at the Boston Foundation who helps lead economic development initiatives in Roxbury. “But you’d think, given all the scrutiny these tech companies are falling under for a lack of empathy and inclusiveness, that they’d be more aware of the optics.’’

The episode, Cox added, is “indicative of a larger problem, which is tone-deafness by a lot of these companies. It’s got to change.’’

Earlier Tuesday, Boston Mayor Martin J. Walsh and US Senator Edward J. Markey had joined residents and business leaders in condemning Amazon’s exclusion of Roxbury; Walsh said Amazon had refused his administration’s initial request to change the practice, leaving “a hole right in the heart of our city.’’

In a statement later Tuesday, the mayor said he was pleased with the company’s about-face.

“After speaking personally with the executives at Amazon, the company informed me today that they will now be offering same-day service to every neighborhood in Boston,’’ Walsh said. “I thank Amazon for this decision, and look forward to its implementation.’’

An Amazon spokesman declined to answer questions about the company’s decision and whether it would make similar changes in other cities.

Reporters at Bloomberg found that ZIP codes whose residents are predominantly black had been conspicuously excluded in six of the 27 metropolitan areas where Amazon offers same-day delivery, including Atlanta, Chicago, Dallas, and Washington, D.C.

Bloomberg said the “most striking’’ example of the pattern was in Boston.

Last week, Amazon said it considers only logistics and the number of Amazon Prime subscribers in an area before deciding whether to offer same-day delivery there.

A Globe analysis of Census Bureau data found that the three ZIP codes excluded from same-day delivery by Amazon had median household incomes below $33,000, compared with $54,485 for all of Boston. All three have more nonwhite residents than white residents.

However, the Boston ZIP code with the highest proportion of black residents, in Mattapan, does receive Amazon same-day delivery, as do nearby majority-minority cities such as Chelsea. That suggests Amazon may have drawn its boundaries based on income or the number of Prime subscribers, not race.

Still, the Bloomberg report noted that while launching the service in areas with the most subscribers may be perfectly logical, “a solely data-driven calculation that looks at numbers instead of people can reinforce long-entrenched inequality in access to retail services.’’

Community leaders and Roxbury residents echoed that sentiment, saying Amazon’s cold, data-driven approach could be used to justify any number of practices that, taken together, would perpetuate existing inequalities. Many saw Roxbury’s exclusion from same-day delivery as just the latest example of the second-class services they often receive from businesses.

“The consensus on the streets was, this was not well thought-out. A lot of folks felt slighted,’’ Cox said. “You’re dealing with communities that, historically, have been overlooked anyway.’’

Former state treasurer Steven Grossman, now chief executive of the Roxbury nonprofit Initiative for a Competitive Inner City, said that Amazon’s data and algorithms may not reflect a recent surge of development in the neighborhood. He also said the company overlooked the economic potential of urban neighborhoods with low income levels but high density.

“Inner cities have their own competitive advantages,’’ Grossman said. “There’s enormous aggregate purchasing power in Roxbury because of the density. If Amazon plays its cards right, it can make a lot of money doing business there.’’

Grossman added that Amazon’s retreat is a cautionary tale for other companies that avoid doing business in certain neighborhoods. He noted that backlash came not just from within Roxbury, but also from other customers who weren’t affected but objected nonetheless.

“The combination of voices that have arisen in a virtually unanimous chorus got the attention of the company’s leadership,’’ he said. “It goes to show that no matter how big and powerful you are, sometimes you have to acknowledge a mistake, show a little humility, and change your practices.’’

Dan Adams can be reached at dadams@globe.com. Follow him on Twitter @DanielAdams86.