"We're not going down. We're going to win this game tonight," Bosh said Sunday. "We're going to come. We prepare like we need to do. Plain and simple, we're going to win this game."
Asked if he was guaranteeing a victory, Bosh said: "I don't care about guarantees. We're just going to win the game."
The Spurs are the 32nd team in NBA history to hold a 3-1 lead in the Finals. All 31 of the previous teams have won the title.
On Saturday, LeBron James said there's no reason the two-time defending NBA champions can't make history by becoming the first to achieve such a feat.
"Why not us? History is broken all the time," James said. "And obviously we know we're against the greatest of odds. No team has ever come back from a 3-1 deficit in the Finals, but there was a point where no team came back from a 2-0. There was a point where no team came back from a 3-0. There was a point where no team came back from a 3-1 or 3-0 deficit in the ALCS, and then the Red Sox did it against the Yankees.
"So history is made to be broken, and why not me be a part of it? That would be great. That would be a great storyline, right? But we'll see what happens. I've got to live in the moment, though, before we even get to that point."
San Antonio has taken command in stunning fashion by not just winning in Miami, but winning twice -- and in convincing fashion. The Spurs won Games 3 and 4 on the road by a combined 40 points, never trailing by more than two in either contest and running out to 25-point leads in each.
The Associated Press contributed to this report.