SOMERVILLE, Mass. — In an office here with the trappings of a Silicon Valley tech firm, a band of politically engaged twentysomethings has built a formidable Democratic fund-raising machine that is fueling the insurgent presidential campaign of Senator Bernie Sanders against Hillary Rodham Clinton and leaving even Republican rivals envious.

The success of the Boston-area outfit, a nonprofit called ActBlue, can be seen most starkly in the latest fund-raising report filed by Mr. Sanders, its most prominent political client at the moment. A whopping 74 percent of the $26 million that Mr. Sanders raised came through ActBlue, an online platform that lets people donate a few dollars at a time to Democrats — and Democrats only — with just a few clicks. Eighty-eight percent of contributions to Mr. Sanders came from donations of $200 or less.

“They’ve obviously found a successful formula that works with their base,” Benjamin Ginsberg, a prominent Republican campaign lawyer in Washington, said. “We don’t have something like ActBlue. We wish we did.”

The speed and sophistication of the 11-year-old operation have given Mr. Sanders a huge edge in the race to gather support from smaller donors, an important test of how well candidates connect with grass-roots voters.