Kevin Durant scored 31 points for the Warriors, who have the opportunity on Friday to become the first team to go unbeaten en route to a title.
Cleveland led by six points with three minutes to play but Durant led an impressive 11-0 run to secure the win.
No team has come from 3-0 down to win an NBA play-off series in 126 attempts.
Only eight teams have swept their opponents 4-0 in the NBA Finals – the last was San Antonio Spurs against Cleveland in the 2006-07 season.
Last season, Golden State eclipsed Michael Jordan’s 1996 Chicago Bulls to set a new NBA record with 73 wins in a regular season.
This term they have become the first team from the United States’ four major professional sports leagues – the NFL, NBA, MLB and NHL – to win 15 successive post-season games.
Game 3 Final Score:Warriors 118, Cavaliers 113 | Warriors lead series 3-0