Golden State, trying to win the Larry O'Brien Trophy for the third time in four years, leads the best-of-seven series, 3-0. Game 4 is Friday night in Cleveland.
Neither team led by more than three points in the fourth quarter until Stephen Curry drained a 3-pointer with 2:38 remaining for a 101-97 Warriors edge.
LeBron James then made a three of his own to make it a one-point game before Andre Iguodala, making his return after missing the previous six games due to a bone bruise in his left knee, converted a dunk to increase the lead to 103-100.
Durant then buried a 3-pointer from 33 feet out with 49.8 seconds remaining to essentially ice the game.
"That was amazing what he did out there tonight," Warriors coach Steve Kerr said of Durant postgame. "Some of those shots, I don't think anybody in the world can hit those but him."
James led the Cavaliers with 33 points. He added 10 rebounds and 11 assists for a triple-double, his fourth of the playoffs.
Rodney Hood, who sat out three games before playing four minutes of garbage time in Game 2 of the Finals, came off the bench to score 15 points for the Cavaliers.
Cavaliers coach Tyronn Lue after practice Tuesday said getting off to a fast start would be critical. He also wanted his team to be more physical than they were in the two games played on Golden State's floor to start the series.
The Cavs led 14-4 with 7:57 left in the first quarter, a complete flip from Game 2 when the Warriors jumped to a 15-6 lead with 8:12 left in the first quarter. The Cavaliers never recovered, even though more than 44 minutes remained.
The difference Wednesday was the Warriors chipped away at the Cavaliers' lead and tied the score 26-26 on a pull-up jumper by Kevin Durant with 32.6 seconds left in the opening quarter.
The Cavaliers regained control in the second quarter by dominating the glass and playing smothering defense on Curry.
Curry scored 33 points and was 9-of-17 on 3-point attempts in Golden State's 122-103 victory in Game 2. He had just two points in the first half of Game 3
and was 0-for-5 on 3-point attempts when the Warriors went to the locker room at halftime trailing 58-52. Curry finished with 11 points.
As they've done throughout the playoffs, the Warriors surged in the third quarter, outscoring the Cavaliers 31-23 to take an 83-81 lead into the fourth quarter. Durant scored 10 points in the third quarter.