Kevin Love came up big, too.
Frye scored 27 points and the Cavaliers kept up their 3-point barrage Friday night, dominating down the stretch for a 121-108 victory that gave Cleveland a commanding 3-0 lead in the Eastern Conference semifinals.
"We're a team that's destined for greatness," James said.
Certainly, the Cavaliers will be hard to stop if Frye plays like he did in Game 3.
Acquired from Orlando in February to provide another outside threat and extend defenses, the 32-year-old played that role to perfection. He made 10 of 13 shots, including 7 of 9 from 3-point range.
It was a devastating blow for an Atlanta team that already was outgunned by the Cavaliers and couldn't cope with someone else stepping into a lead role.
"We brought him here to shoot," James said. "And shoot and shoot and shoot."
Two nights after setting an NBA record with 25 baskets beyond the arc, the Cavaliers were nearly as good in a 21-of-39 performance that moved them within one victory of their second playoff sweep over the Hawks in two years.
Atlanta turned in a much more respectable showing after getting blown out in Game 2. But in the end, it was the same result for a team that has lost 10 straight to the Cavaliers going back to last year's conference final.
Game 4 is Sunday in Atlanta, but this was likely the last chance to make it a competitive series.
"We're fighting for our playoff lives right now," Al Horford said. "At this point, we have to do some changes, because what we've done hasn't worked."
The Hawks led by as many as 11. Turns out, that wasn't nearly enough to hold off the Cavaliers.
James and Irving each scored 24 points, while Love chipped in with 21.
Then there was Frye, whose previous high in these playoffs was 12 points and best showing ever in the postseason was a 20-point effort in 2010, when he played for Phoenix.
Frye relayed some advice from teammate James Jones: "Channing, you've got to stop passing. You're not very good. You've just got to shoot it."
So he did. Over and over again.
The Hawks led 103-99 with just over 8 minutes remaining, but the Cavaliers were relentless and the home team -- which had matched Cleveland shot for shot -- suddenly went cold.
Cleveland went ahead for good when the Hawks inexplicably left James all alone outside the 3-point stripe. He had time to step up to the line, set himself, and put up the jumper. Nothing but net, naturally, giving the Cavaliers their first lead since late in the second quarter.
At the other end, Paul Millsap had a pass knocked away by J.R. Smith, the ball winding up in James' hands. He saw Frye breaking toward the other end, all alone, and fired ahead for a thunderous dunk that extended Cleveland's lead with 5:56 left.
Cleveland scored 22 of the final 27 points, the Hawks making just two of their final 12 shots, with four turnovers mixed in.
The frustration boiled over in the closing seconds. As James attempted to drive, Jeff Teague shoved him into the seats behind the basket with a shoulder shot, drawing a flagrant foul.
Looking for a boost after the Game 2 blowout, the Hawks changed up their lineup. Thabo Sefolosha started in place of struggling Kyle Korver, who reacted to the demotion with his best game of the series.
Korver scored 18 points and made 5 of 9 from 3-point range. Horford led the Hawks with 24 points, also his best showing of the series. On top of that, the Hawks got some valuable minutes out of little-used reserve Kris Humphries, who had nine points and four rebounds.
It didn't matter.
The Cavaliers outrebounded the Hawks by a staggering 55-28 margin.
Love had 15 rebounds, while James and Tristan Thompson grabbed 13 apiece.
No one on the Hawks had more than eight.
Hawks coach Mike Budenholzer shrugged off the huge deficit, pointing out the Cavaliers had a 30-14 edge at halftime but still trailed 63-55.
"Obviously, you don't want to be outrebounded. You don't go into a game saying, `Go ahead, take them all," he said. "But we outrebounded them in the first game and lost. I think what matters more is who scores the most."
Cavaliers: Have never lost to Atlanta in the postseason. The victory improved Cleveland's playoff record to 11-0 vs. Atlanta. ... Have yet to lose in these playoffs, either. The Cavs will be going for the second straight sweep, having blown through Detroit in four straight games in the opening round.
Hawks: In his first start of the playoffs, Sefolosha had eight points and four rebounds. ... Millsap made only 7 of 17 shots and finished with 17 points. ... Teague doled out 14 assists to go along with 19 points.