“This is a critical victory for the progressive movement in showing that voters are ready for a new generation of progressive leadership in the Democratic Party,” said Alexandra Rojas, executive director of Justice Democrats. “This isn’t just a loss for one incumbent. It’s a defeat for machine politics and big corporate donors who want to stop our movement for ‘Medicare for all,’ a Green New Deal and reproductive rights.”

Ms. Newman’s victory was a rare bright spot for the progressive movement in Tuesday’s contests, in which Senator Bernie Sanders of Vermont suffered major defeats in three crucial states, including Illinois. The results all but extinguished his hopes of a comeback against former Vice President Joseph R. Biden Jr., who appeared to be headed toward becoming the Democrats’ presumptive nominee.

The race put a fine point on the tensions within the Democratic Party in the era of President Trump. Mr. Lipinski’s views are far more conservative than those of Mr. Biden, and in many ways he was an outlier among Democrats. In addition to voting against the 2010 health care law and opposing abortion rights, he declined to endorse former President Barack Obama in 2012 and opposed same-sex marriage until the Supreme Court made it legal across the nation in 2015.

Despite their official stance that the party backs incumbents, top Democrats did not go out of their way to advance Mr. Lipinski’s cause. During a trip to Texas last month, with 10 days to go until the state’s primary, Speaker Nancy Pelosi dropped in on the campaign offices of another conservative Democrat, Representative Henry Cuellar, boosting his successful battle to defeat a Justice Democrats-backed challenger, Jessica Cisneros. Ms. Pelosi did not do the same for Mr. Lipinksi.

And Mr. Lipinski’s fellow Illinoisan, Representative Cheri Bustos, who leads the party’s campaign arm, canceled a planned fund-raiser for Mr. Lipinski last year, bowing to progressives who were outraged by the congressman’s anti-abortion rights stance. Her decision raised questions about whether there was room left in the party for lawmakers who oppose abortion.