Phoenix got back in it with an 11-0 run. Morris scored on a baseline dunk, then followed with a 3-pointer that cut the Clippers' lead to 90-86 with 6:31 left.
Green was 3 for 16 before making two 3s and bouncing in a 16-footer to cut the lead to 97-94 with 2:37 to go. Griffin made a fadeaway 13-footer with 2:09 left.
"The third quarter, they were more physical, especially on defense," Dragic said. "We were catching the ball way out and we didn't get open shots. They just played hard defense, like we should do."
Early on, Phoenix dominated.
The Suns outscored the Clippers 16-2 over the final 3½ minutes of the first quarter and the opening 1:45 of the second to lead 30-24 after newcomer Shavlik Randolph made one of two free throws with 10:15 left in the half.
Dragic got his offense in gear in the final 1:19 of the half. He sank a 3-pointer, stole Barnes' pass for a layup, then fed Alex Len for a layup as Phoenix used a 9-2 run to lead 55-44 at the break.
NOTES: Barbosa was hurt taking a charge late in the first quarter but stayed in the game another 6 minutes. ... Phoenix is a half-game ahead of Memphis for the No. 8 playoff spot in the West. ... The Clippers were without Jamal Crawford (strained left calf) for the second game in a row. ... Len, a first-round draft pick, got his first start in place of Plumlee and struggled with six points and six rebounds in 19 minutes. ... Plumlee injured his knee in practice last week and had been trying to play through it. ... Suns G Eric Bledsoe, coming back from knee surgery, participated in a full scrimmage Monday. ... Bledsoe was hurt in the Suns' 107-88 win over the Clippers in Los Angeles on Dec. 30, the only other time the teams have met this season.