Rep. Debbie Wasserman Schultz, the Florida Democrat who was pressured into giving up her post as chair of the national party on the eve of its presidential convention, survived a high-profile primary challenge for her House seat Tuesday.

The six-term lawmaker soundly defeated Tim Canova, a law professor who campaigned to Ms. Wasserman Schultz’s left with the backing of Vermont Sen. Bernie Sanders. Ms. Wasserman Schultz was sidelined as the party’s leader in the wake of hacked Democratic National Committee emails that suggested...