Houston's 99-93 Game 5 win came in Los Angeles and sends the first-round series back to Texas for Friday's Game 6.
The victory gives the Rockets a second straight win after falling behind 3-0, keeping alive a comeback no NBA team has completed in a best-of-seven series.
Of 159 series that began 3-0, only four teams have forced a Game 7, underscoring the scale of Houston's task despite renewed pressure on the Lakers.
Are the Lakers' 'unplayable' reserves the real reason their title hopes are fading?
Was Houston's three-point barrage a fluke or a fatal flaw in the Lakers' defense?
Can Coach Redick's adjustments prevent the Lakers from a historic playoff collapse?
Is LeBron James' fourth-quarter fade a sign of fatigue or a larger team issue?
How much is Luka Dončić's absence truly costing the struggling Los Angeles Lakers?
How are the Rockets thriving in the playoffs without their superstar Kevin Durant?