The Warriors managed just 40 second-half points before their final 11-point flurry.
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.
James scored 12 points on 4-13 attempts from the field and went scoreless in the last three minutes of the game.
The only suspense left is whether LeBron James and the Cavs will be able to take a game in the series.
The Cavs set scoring records in the first half and then held on during a wild third and fourth quarter that included technical fouls, James jawing with fellow superstar Kevin Durant and Cleveland's crowd roaring like a jet engine. There were also 76,680,000 total minutes streamed - all records for an NBA Finals Game 3.
Cleveland coach Tyronn Lue decided not to change his starting lineup for Game 3, sticking with the slumping Smith at shooting guard.
"I said it after we won the Eastern Conference finals that we're getting ready for a juggernaut", LeBron James said during Wednesday's postgame press conference.
They will again have to rewrite the record books if they can recover this position, but with the Warriors seeking revenge for past year that will be some ask.
Golden State landed the next blows, but the Cavs kept coming back. There is, however, some solace in the fact that.More news: Trump cheerleaders turn on special counsel Mueller
IS COMEBACK REAL? The defending champion Cavs came back from a 3-1 deficit last season, but things seem very different in 2017. So we have already witnessed history.
If beat the Cavaliers in Game 4 in Cleveland's Quicken Loans Arena, they will be the first team to go undefeated in an National Basketball Association playoffs.
The good news for Green is it looks like the Warriors will continue to reap the rewards of his recruiting work as well. At least when LeBron joined Dwyane Wade in Miami they had some adversity and lost in the 2011 Finals.
The heartache, as much as the addition of star forward Durant, has made the Warriors all the more stronger now, even in snatching defeat from victory's jaws past year. However, barring a bout of ideal execution, Cleveland doesn't look equipped to be able to avoid the four-game death sentence Golden State is looking to dish out.
Durant's team mates were singing his praises after the game and said there was no doubt in their minds whose hands the ball should be in with the game's result hanging in the balance.
Expect another big game from James, and Cleveland won't go down without a fight, but it likely won't be enough to keep their now slim championship hopes alive.
The Warriors closed the first quarter on a 10-0 run and led 39-32. "It will be a massive upset, I think, if they're not there each and every year".
With their 15 consecutive wins, no team has come as close to perfection as the Warriors have.