The US women easily took the first two sets, but allowed two-time champions China back into the final which they won 27-25, 25-20, 16-25, 26-24.
Hill scored 20 points in the game and was then named most valuable player and best spiker of the tournament
She smashed the winning point that sparked wild celebrations among the US women.
“We came here to make history and we made it. It was a tough battle,” said US coach Karch Kiraly, who won Olympic golds himself in men’s volleyball and beach volleyball.
“After we got a 2-0 lead we knew China would never give up. It was a battle to the end and they have some great young players, as do we.
“I hope that we will be playing against each other in the future. It is just good for the sport to have teams with such history performing at a high level.”
The United States’ women, who before Sunday had never won an Olympic, World Cup or world championship title, should become world number one when new rankings come out this week.
Runners up in the world championship in 1967 and 2002 and beaten by Brazil at the last two Olympic finals, Sunday’s victory is a vital springboard to aim for US success at the Rio de Janeiro Olympics in two years.
The United States scored an upset win over Brazil in Saturday’s semi-finals.
China’s coach Ping Lang won the gold medal with Chinese team at the 1984 Los Angeles Olympics and then coached the US team to silver at the 2008 Beijing Games.
She said she was looking for a year of “good training” with her young team ahead of the Rio Olympics.
Brazil claimed the third-place play-off thanks to a 3-2 (25-15, 25-13, 22-25, 22-25, 15-7) win over hosts Italy.