INDIANAPOLIS — Greg Pence, the oldest brother of Vice President Mike Pence, won the Republican primary on Tuesday for the Indiana House seat once held by his more famous sibling, successfully leveraging his family name into prodigious fund-raising and ample votes that make him a heavy favorite to win the seat in November.

In his first run for public office, Mr. Pence, 61, ran a largely hermetic race, declining to debate his opponents and refusing most requests for interviews. Instead he made the rounds of Lincoln Day dinners and met quietly with voters in a district that stretches from Muncie to the north to the Ohio River to the south.

“I’m ready to serve again,” Mr. Pence, who enlisted in the Marines after college, said to a cheering crowd in his hometown, Columbus.

[Get full results from Indiana’s primary elections here.]

His closest challenger was Jonathan Lamb, who owns several small businesses and was the only candidate close to being financially competitive with Mr. Pence. The victor ultimately used connections to his brother and President Trump to raise more than $1 million for his race, an unmatchable figure.