The Democrats’ liberal wing scored few wins in Tuesday’s primaries as it challenged more-centrist candidates.

The Democrats’ vocal, liberal wing sought to ride rising party enthusiasm to upset victories over more-centrist candidates or incumbents in Tuesday’s primaries across four states. But it scored only a few wins. Instead, a big winner of the night was Emily’s List, a Democratic group whose candidates have at times challenged those backed by liberal firebrands Sen. Bernie Sanders and Alexandria Ocasio-Cortez, whose upset primary victory against Rep. Joe Crowley (D., N.Y.) propelled her to national recognition. Of the Tuesday races that have been called so far, 27 of the 28 candidates supported by Emily’s List won their races, said Stephanie Schriock, president of the group, which backs only women. “I think a lot of our women are very practical progressives,” Ms. Schriock said. “Voters, they get promises all the time and they’re tired because then nothing happens. What they’re looking for now is someone to make the place work.”

In Michigan’s Democratic gubernatorial primary, Gretchen Whitmer, formerly the Democratic leader in the Michigan state Senate, bested two candidates who ran to her political left: Abdul El-Sayed and Shri Thanedar. Ms. Ocasio-Cortez campaigned with Mr. El-Sayed, a physician who was aiming to become the nation’s first Muslim governor.

In a crowded Kansas primary to challenge Republican Rep. Kevin Yoder this November, Ms. Ocasio-Cortez and Mr. Sanders backed labor lawyer Brent Welder. Mr. Welder lost the nomination to Sharice Davids, an attorney and former mixed martial arts fighter who was supported by Emily’s List. And in Missouri and Washington state, a few long-shot candidates fell short in their bids to oust longtime incumbents in heavily Democratic districts in St. Louis and Seattle. Ms. Ocasio-Cortez backed Cori Bush, a registered nurse and activist, in her primary challenge to Democratic Rep. Lacy Clay of Missouri. Mr. Clay sailed to victory over Ms. Bush and is poised to be re-elected this November.

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