The victory trimmed Golden State's deficit in the best-of-seven to 3-2, with the series returning to Oklahoma City for another possible close-out game for the Thunder on Saturday night.
Game 7, if necessary, would be Monday in Oakland.
Stephen Curry poured in 31 points, going 10-for-10 from the free-throw line, as the Warriors overcame a 40-point explosion by Thunder star Kevin Durant to keep their hopes of a title repeat alive.
The Warriors led just 81-77 before backup guard Shaun Livingston opened the fourth period with a short jumper.
Iguodala and Barnes then nailed their 3-pointers, opening an 89-77 advantage, Golden State's biggest lead of the game to that point.
The advantage reached 13, but power forward Serge Ibaka wouldn't let the Thunder go quietly. He swished a pair of 3-pointers, and when Durant added a third, all of a sudden Golden State's lead was just 103-98 with still 4:34 to go.
Curry then responded with his biggest hoop of the night, a driving left-handed floater on which he was fouled. He converted the three-point play, pushing the lead to eight.
The Golden State defense took it from there, holding the Thunder without a field goal until a Durant dunk with 56.9 seconds left, by which point the Warriors had pulled away into a commanding 112-101 advantage.
Klay Thompson overcame 2-for-9 shooting on 3-pointers to back Curry with 27 points for the Warriors, who are now 4-1 after losses in the playoffs.
The Warriors won despite making just nine of their 24 3-point attempts.
Andrew Bogut had 15 points and a game-high 14 rebounds, and Draymond Green had an 11-point, 13-rebound double-double for the Warriors.
The Warriors shot 47.1 percent for the game to 42.9 percent for Oklahoma City. Golden State battled the Thunder even on the boards, 45-45.
Durant's 40 points came on 12-for-31 shooting. Like Curry, he did serious damage at the free-throw line, going 13-for-13.
Russell Westbrook backed Durant with 31 points to go with seven rebounds and a team-high eight assists.
Ibaka had 13 points and Steven Adams a team-high 10 rebounds for the Thunder, who were able to eliminated Dallas and San Antonio in earlier series at first opportunity.
The Thunder made 13 of their 30 3-point attempts, outscoring the Warriors 39-27 from beyond the arc.
