The votes are still being counted, but this much is clear: Mexico’s leftist governing party dominated Sunday’s elections.

Claudia Sheinbaum, the first woman and first Jewish person to be elected president, beat her opponent on Sunday by a stunning 30 percentage points or more, early returns show. She and her Morena party were expected to win, but they outperformed pre-election polls: She won a larger share of the vote than any presidential candidate in decades, and her party and its allies are within reach of claiming big enough majorities in Congress to enact constitutional changes that have alarmed the opposition.

Preliminary results show Morena taking seven of the nine governorships up for grabs — including the most prominent, Mexico City’s — and winning supermajorities in at least 22 of the 32 state legislatures.

The election served as a referendum on the nearly six-year term of Andrés Manuel López Obrador, the current president, reflecting that a solid majority of the electorate has endorsed his stewardship of the country.

“We’re taking the whole shebang in these elections,” Mario Delgado, the head of the Morena party, said in a speech Sunday.

During Mr. López Obrador’s tenure, millions of people were brought out of poverty, the minimum wage doubled and pensions became available to many more Mexicans. But he also empowered the military, prioritized fossil fuels and pushed measures that critics say could weaken Mexico’s democratic institutions.