MEXICO CITY—Mexico’s Senate overwhelmingly voted for a broad rewrite of trade rules between the United States, Canada and Mexico—making the nation the first of the three partners to ratify the pact designed to replace the North American Free Trade Agreement.

Senators voted 114-4 with three abstentions on Wednesday to ratify the accord—rebranded as the U.S.-Mexico-Canada Agreement, or USMCA—which was signed last November by the heads of state of the three countries. Easy passage of the trade pact by the Mexican lawmakers was...