Jackson (7-4) allowed four hits, including Ryan Garko's homer. The right-hander stopped a five-start winless stretch, earning his first victory since June 6.
"He was tremendous," Tigers manager Jim Leyland said. "That's a pretty good showing to do what he did tonight."
Jackson threw as hard as 96 mph but recorded most of his outs on easy fly balls or grounders. He struck out four and walked two.
"Strikeouts will come, but you want quick outs all the time," Jackson said. "You have to pitch to contact."
The Indians put runners on second and third with one out in the eighth, but Bobby Seay struck out Shin-Soo Choo and got Travis Hafner to pop out. Fernando Rodney loaded the bases with two outs in the ninth but retired Grady Sizemore on a groundout to third to end the game.
Lee (4-9) gave up three runs and five hits in seven innings. The reigning AL Cy Young Award winner lost his third consecutive start despite striking out eight.
"I was disappointed we couldn't get any runs for him," Indians manager Eric Wedge said. "But he pitched like the No. 1 he is. He does everything he can do to win games for us."
Lee's only bad inning was the second. All-Star Brandon Inge and Magglio Ordonez opened with singles. Gerald Laird then hit an RBI double. After Adam Everett struck out, Anderson singled in a pair to make it 3-0.
"I can only control what I can control," said Lee, who hasn't won since he shut out St. Louis on June 14. "I can't score runs for us, which has been a problem for us all season."
Cleveland is averaging less than four runs per game in Lee's 20 starts.
Anderson did not return to center field after Lee hit him with a pitch in the fifth. The Tigers said he had a bruised right triceps.
Detroit reliever Joel Zumaya threw just two pitches in the eighth before leaving with a cut on the top of his right thumb.
Tigers OF Carlos Guillen (shoulder) could start a rehab assignment as early as this weekend. "He really looks good," Leyland said of Guillen, who's been out since May 5. "You can tell by looking at him that he feels good." ... Indians RHP Jake Westbrook (Tommy John surgery) threw 50 pitches in Cleveland. Trainer Lonnie Soloff said the session went well and Westbrook will go through a similar workout Monday. ... Inge will take part in Monday's home run derby. ... Garko and Detroit's Miguel Cabrera each extended their hitting streaks to 10 games. ... Cleveland signed OF Jason Kipnis, its second-round draft pick.