The Rockets became just the ninth team in NBA history to overturn a 3-1 playoff deficit as they eliminated a Clippers outfit that had looked dominant early in the series.
James Harden tallied 31 points, seven rebounds and eight assists for Houston, while centre Dwight Howard added a double-double of 16 points and 15 rebounds.
The Rockets never trailed on the night, but they endured a nervy close to the fourth quarter. Blake Griffin scored five points in a 9-0 run that saw the Clippers move within eight points. Harden made a pair of free throws in response, but a dunk by DeAndre Jordan saw the Clippers once again cut the margin to just eight.
Trevor Ariza then buried a corner three-pointer with just under a minute remaining to calm Rockets nerves. Ariza finished with 22 points and made six three-pointers.
For the Clippers, Griffin had 27 points and Chris Paul had 26 points and 10 assists.
The Rockets will face the Golden State Warriors in the Western Conference finals, with Game 1 getting underway on Tuesday.