Ms. Hayes’s victory is particularly significant, given the current dynamics of the Democratic Party.

She won handily over an opponent who was a longtime member of the Connecticut Democratic establishment, buoyed by a progressive platform that included an embrace of “Medicare-for-all,” explicit support for racial justice and a pledge to not vote for the current minority leader, Nancy Pelosi, for speaker of the House should the Democrats take back control.

She continued a trend in which progressives have experienced their biggest wins in safe Democratic districts. While progressives running in statewide races like Abdul El-Sayed have not been successful (he lost last week in Michigan), Ms. Hayes is in the mold of victorious progressives like Alexandria Ocasio-Cortez, the New York City activist who beat longtime Representative Joseph Crowley in a June primary.

In both of these cases — as with Ms. Omar and Ms. Hayes — Democratic voters have shown themselves more likely to opt for progressive candidates in districts that will be reliably blue come November.