Signed as a free agent on January 15, Jackson replaced injured point guard Steve Francis and made his second start in 41 games.
Houston (45-36) never trailed but nearly let a 20-point lead slip away. The Rockets took an 84-64 lead with 3:22 left in the third quarter and still had a 96-87 advantage with 5:11 left in the fourth.
Seattle climbed within 105-103 with 12 seconds remaining on a 3-pointer by Vladimir Radmanovic. The Sonics used a barrage of 3-pointers to climb back into it during a 35-point fourth quarter.
Mark Jackson, 39, made 4-of-8 shots, including 3-of-7 from the arc. He also dished out nine assists and made 14-of-17 free throws, including four in the final 12 seconds.
Six Rockets reached double figures, including Scott Padgett and Bostjan Nachbar, who got rare starts. Padgett scored 12 points and Nachbar chipped in 11, making a clutch 3-pointer with 12.8 seconds left that helped turn back the SuperSonics' comeback.