Tammy Murphy, the first lady of New Jersey, gained crucial support in her bid for the U.S. Senate on Monday night, winning the Democratic convention vote in Bergen County by a decisive margin.

It was Ms. Murphy’s first victory at a convention decided by delegates using secret ballots, and it was considered a must-win matchup in her primary battle against Representative Andy Kim, a third-term South Jersey Democrat.

The vote was 738 for Ms. Murphy, 419 for Mr. Kim.

Over the past month, Mr. Kim, 41, won the first five county conventions in New Jersey that permitted delegates to select a nominee, including in Monmouth County, where Ms. Murphy and her husband, Gov. Philip D. Murphy, have lived for 25 years.

With the support of Mr. Murphy, who has nearly two years left in his term, Ms. Murphy, 58, racked up early endorsements from a raft of influential Democratic officials even before hitting the campaign trail.

But she has been battered by claims of nepotism and has struggled to gain support among rank-and-file Democrats as she makes her case that she should be their nominee to run for a coveted seat now held by Senator Robert Menendez, a Democrat who has been charged with taking bribes. Mr. Menendez has not ruled out running for re-election, but he has been abandoned by most Democratic leaders and has almost no path to victory.

Bergen County, in northern New Jersey, is the state’s most populous region. It has more Democrats than any county other than Essex, which includes Newark, the state’s largest city.