Randy Foye scored a season-high 20 points and DeAndre Jordan grabbed 12 rebounds for the Clippers, who shot 36.4 percent (32 of 88) and mustered only 10 points in the final quarter to drop their fourth straight road game.
Griffin scored 14 points and pulled down 11 rebounds. But he went 5 for 16 from the field with Hayes, Houston's best low-post defender, guarding him all night.
The 6-foot-10 Griffin made his first basket on his 101st dunk of the season, an easy one-hander following an offensive rebound with 7:40 left in the first quarter.
But with the bulky Hayes pushing him away from the basket, Griffin was quiet the rest of the half, going 2 for 7 from the field and grabbing four rebounds.
Scola scored 10 points in the opening quarter and Houston headed to the second with a 27-22 lead.
The Clippers' reserves rallied from seven points down to take a 44-42 lead with five minutes left before the break. Both starting lineups were back on the floor for the last four minutes, and Hayes' layup with 8 seconds left gave Houston a 55-52 lead at halftime.
Jordan threw down a one-handed dunk with 8:35 left in the third quarter, off Griffin's assist, to cut the Rockets' lead to 59-58.
The teams combined for eight turnovers in the first eight minutes of the sloppy third quarter. The Rockets missed 12 of their first 15 shots after halftime, and the Clippers took a 70-65 when Foye set a new season high with consecutive driving layups.
Houston went 4 for 19 from the field in the third, but only trailed 73-70 because the Clippers gave away six turnovers in the quarter.
The Rockets extended their lead to nine as the Clippers missed their first 15 shots in the last quarter, many of them uncontested tries from close range. Baron Davis ended the Clippers' drought with a short jumper with 5:43 remaining.
Houston rookie Patrick Patterson flipped in a hook shot and Brooks drove for a layup to extend the Rockets' lead into double digits for the first time at 86-75.
Notes: The Rockets have won 11 of the last 14 meetings with the Clippers in Houston. ... The Clippers were outrebounded (50-44) for the first time in eight games. ... Griffin has 37 doubles-doubles this season. ... Griffin wore a black sleeve on his left arm to protect the elbow he hurt on a hard foul by Dallas' Brendan Haywood on Tuesday night. ... Referee David Jones twisted his left knee running down the court in the third quarter. Both trainers chatted with him during a timeout early in the fourth, but Jones stayed in the game. ... The Rockets held an opponent under 100 points for the third time since Dec. 22 — when they beat the Clippers 97-92 at the Staples Center.