Griffin led six Detroit players in double figures, finishing with 26 points, 10 rebounds and nine assists before sitting out most of the final quarter.
Jackson was back in the Detroit starting lineup after missing 24 games with a severe ankle sprain. He scored seven points on 3-of-7 shooting in 15 minutes.
Luke Kennard added 16 points and Ish Smith 13 for the Pistons.
The Suns were without their two leading scorers. Devin Booker missed his second straight game with a right-hand sprain and T.J. Warren was out with left knee inflammation after being hurt late in Saturday night's loss to Golden State.
Alex Len led Phoenix with 19 points and 12 rebounds. Troy Daniels added 18 points, going 4 of 5 on 3-pointers, and Josh Jackson had 15 points and 11 boards for the Suns, who have lost 24 of 26 to run their NBA worst-record to 19-53.
Detroit has won the last two after dropping the first three of a six-game road trip that ends Thursday night in Houston.
Neither team led by more than seven points and both had trouble making shots in the first half, with the Pistons up 44-38 at the break.
The Pistons shot just 32 percent (15 for 47) and Phoenix 36 percent (17 for 47) in the first two quarters. The Suns made only two of 18 3-pointers in the first half to Detroit's 5-of-16 effort.
Griffin's 16 points led all first-half scorers while Len had 13 points and eight rebounds.
The Pistons blew open a 21-point lead in the third quarter, outscoring Phoenix 25-10 go to up 69-48 with 4:56 left in the period. Seldom-used Alec Peters' 3-pointer cut it to 77-64 but Anthony Toliver sank his third 3-pointer in the final four minutes of the quarter to put Detroit up 80-64 entering the fourth.
The Pistons led by as many as 30 in the fourth quarter.
Pistons: Jackson had been ruled out for the game by coach Stan Van Gundy at the shootaround but that changed when the coach met with the media pregame. ... Griffin, who made his first appearance against Phoenix as a Piston, averaged 22.5 points and 8.2 rebounds in 26 career games against the Suns as a Los Angeles Clipper.
Suns: Phoenix has lost 10 in a row at home. ... Suns assigned C Alan Williams to Northern Arizona of the G-League. Williams is coming back from September knee surgery. ... Jackson's 36 points against Golden State on Saturday was fourth-most points by a rookie this season. ... Booker missed his 18th game of the season. ... Phoenix has won five games since Christmas, one since Jan. 31. ... Dragan Bender made 1-of-8 3s. ... Other than Daniels, the Suns were a combined 3 of 29 on 3s.
Pistons: at Houston Thursday night.
Suns: at Cleveland Friday night.