Representative Andy Kim, a third-term Democratic congressman, won an early but significant victory on Saturday against New Jersey’s first lady, Tammy Murphy, as they compete in one of the country’s most closely watched Senate primaries.

Mr. Kim, 41, was selected as the Democratic Party’s nominee in Monmouth County during the first convention of its kind this election cycle — a high-stakes affair that drew a standing-room-only crowd of delegates to the Portuguese Club of Long Branch, a 32,000-person seaside community.

It was a win laden with symbolism. Ms. Murphy, 58, lives in Monmouth County, and Mr. Kim represents a large swath of the affluent, predominantly coastal region.

In September, the dean of the state’s Democrats, Senator Robert Menendez, was charged with taking bribes for the second time in 10 years, creating a rare opportunity for challengers to vie for the coveted seat. Mr. Menendez has not ruled out running for re-election, but he did not compete for the Monmouth County nomination. Two other candidates, Patricia Campos-Medina, a union leader, and Larry Hamm, a Newark-based social justice activist, won nominal support Saturday. (Mr. Hamm withdrew from contention Saturday, a county leader told delegates, but his name remained on the ballot.)

The federal prosecution of Mr. Menendez has provided a sordid backdrop to the race, contributing to its early intensity and adding fuel to Mr. Kim’s pledge to interrupt the state’s entrenched political patronage system and restore dignity to the party.

“The challenges we face are deep to the bone of our country,” Mr. Kim said in a speech to delegates, adding, “Ask yourself: We have wars abroad and turmoil here. Who is ready to lead our country?”