Oklahoma City had a chance as the final seconds ticked away, but a failed drive by Reggie Jackson and a missed put-back attempt by Serge Ibaka resulted in Houston taking its first win in the series.
The Rockets, fueled by a monster third quarter, held off the Thunder for a 105-103 victory at the Toyota Center to escape elimination.
After Oklahoma City led by as many as 13 points and went into halftime with a six-point lead, Houston came out hot in the third, winning the quarter 38-24.
During the third Houston took its first double-digit lead of the entire series, putting the Thunder in a hole that proved too hard to climb out of without Russell Westbrook in the lineup and Kevin Durant facing constant double teams.
Houston has led in the fourth quarter the two previous games only to see the Thunder charge back to win and it almost happened again on Monday night.
Durant scored five quick points, capped by a massive dunk over center Omer Asik, to cut the Houston lead to two points with 1:13 remaining in the contest. However, neither team would score again in the final minute, as Ibaka's put-back attempt rolled off as the final buzzer sounded.
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Durant led the way for Oklahoma City again, albeit in a losing effort, with a game-high 38 points on 12-of-16 shooting and a 13-of-15 performance from the foul line. KD chipped in eight rebounds and six assists but also turned the ball over seven times.
Jackson continued to fill in well for Westbrook with 18 points, four rebounds and three assists, but he struggled from the floor on 7-of-18 shooting.
Kevin Martin played a big role in a dominant second-quarter effort from the Thunder and had 14 points at the break, but he once again disappeared for OKC in the second half with just two points.
Chandler Parsons led Houston with 27 points and Patrick Beverley had 16. James Harden was held in check with 15 points on 4-of-12 shooting with 10 turnovers.
The teams were almost identical statistically, as OKC shot 48.6 percent to Houston's 48.7 and the teams shot 44 percent and 44.4 percent from 3-point range, respectively. But the Rockets doubled up the Thunder underneath, outscoring Oklahoma City 44-22 in the paint.
With the series now 3-1 in favor of the top-seeded Thunder, the play returns to Chesapeake Energy Arena for Game 5. Tipoff is set for 8:30 p.m. on Wednesday.