The Rockets have not won three in a row since a four-game winning streak from January 11-17.
On Saturday, Houston defeated New Jersey, 83-71, behind a superlative defensive performance.
The Rockets limited the Nets to just 24 points in the first half - the Rockets’ best defensive half in franchise history - and 36 percent shooting overall.
Houston is one-half game behind Phoenix for the eighth and final Western Conference playoff spot.
The Clippers have lost nine of 10 and fell to 1-3 on their season-high six-game road trip with a 95-86 setback at Atlanta on Monday.
Corey Maggette scored 14 points in the first quarter but managed just five the rest of the game after spraining an ankle.
The Clippers are just 1-4 under interim coach Dennis Johnson.
Los Angeles has won a franchise-record five straight games over Houston, including the first two meetings this season. The Clippers won here on December 14, 94-85.