The former Arizona state senator Debbie Lesko fended off an energetic Democratic challenge to win the special congressional election on Tuesday, according to The Associated Press.

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Tuesday’s special election in Arizona’s Eighth Congressional District, in the conservative suburbs outside Phoenix, revealed the depth of Republicans’ political challenges in 2018. Ms. Lesko was favored to win over Hiral Tipirneni, a Democrat and emergency room doctor, in a district that supported Donald J. Trump in 2016 by more than 20 points.

Even so, national Republicans spent more than $1 million to help Ms. Lesko. With an outcome this close in a district that should have Republicans winning big, it is another sign of Democratic enthusiasm, organizational muscle and determination to send a message about President Trump and his party.

See the drop in Republican margins in special elections since Donald J. Trump became president.

The congressional seat became vacant this year when Representative Trent Franks resigned amid reports that he pressed female aides to serve as surrogate mothers for Mr. Franks and his wife.