The team from the suburban New Orleans town of River Ridge began its offensive breakthrough in the fifth inning with four runs on four hits.
Marshall Louque had three hits for the club representing the Southwest region, including a pair of doubles that drove in three runs.
Louisiana outfielder Reece Roussel also hit an RBI double. Prior to Sunday, he was 15 for 20 at the plate in South Williamsport, Pa., where the LLWS has been staged each year.
Curacao loaded the bases with one out in the top of the third, but a pair of quick outs left them with nothing.
Prather pitched a complete game, throwing 88 pitches over six innings. He picked up two wins and struck out 19 batters in 14 1/3 over the tournament.
With the win, the team from the East Bank of Jefferson Parish became the first team from Louisiana to win the championship. Sunday's win brought another back-to-back win for the U.S., its first since 2009, when a team from Chula Vista, California, capped off a streak of five straight championships for the United States.
President Trump sent a congratulatory tweet and indicated the team would be invited to the White House.
"Congratulations to Louisiana’s Champions. See you at the White House!" he posted.
The team from Louisiana clawed its way back into the tournament after losing its first game to Hawaii.
It became the first team to win the tournament after losing its opener since the LLWS expanded to 16 teams in 2001.