James, who scored 44 points in his team's series opening loss, again carried the offensive burden with 39 points, 16 rebounds and 11 assists for the Cavaliers, who lost All Star Kyrie Irving to a serious knee injury in Game One.
Irving had surgery on Saturday to repair his fractured left kneecap, a procedure described as successful by the team.
Cleveland's relentless defense held Golden State to 39 percent shooting and made it a forgettable night for regular season MVP Stephen Curry.