The Lakers were 3-0 down in the best-of-seven series but fought back on Saturday to win 119-108 in Los Angeles.
James was supported by Anthony Davis, who registered 25 points and 23 rebounds to end an 11-game losing streak against the Nuggets.
“We’ve given ourselves another life, another lifeline,” James, 39, said.
“The only opportunity for us is just to play the next game.”
James is searching for his fifth NBA title and his first with the Lakers since 2020.
The fifth game takes place in Denver tonight.
In the Eastern Conference, Jayson Tatum scored 22 points with 11 rebounds and six assists in the Boston Celtics’ 104-84 win over the Miami Heat, who were at home.
The Celtics, who are the NBA’s top seeds, lead the series 2-1.
The Orlando Magic beat the Cleveland Cavaliers 112-89 to level their play-off at 2-2, while the Oklahoma City Thunder took a 3-0 lead with a 106-85 victory over the New Orleans Pelicans.