Civale improved to 7-1, becoming the American League's first seven-game winner. St. Louis' Jack Flaherty leads the majors with eight victories.
''I really feel like things are going smoothly right now,'' he said. ''I'm having enough success that I'm not trying to make major adjustments between starts. I can focus on minor things.''
Civale is 6-0 with a 2.19 ERA in seven career starts against the Tigers, including three wins this season. He allowed one run, six hits and a walk in eight-plus innings.
''I'm probably the wrong guy to ask about what he's doing, because we certainly aren't figuring anything out,'' Tigers manager A.J. Hinch said. ''All I know is he's got a lot of pitches we can't hit.''
Civale started the ninth but left after Jeimer Candelario singled and Miguel Cabrera walked.
''That was a great performance,'' Cleveland manager Terry Francona said. ''He moved the ball around and changed speeds like a veteran. He didn't walk anyone until Miggy in the ninth and he could have finished the game if we needed it.''
James Karinchak allowed an RBI single to Jonathan Schoop and walked Akil Baddoo to load the bases with one out. Willi Castro took a called third strike and Eric Haase flew out to give Karinchak his sixth save.
''I knew James was going to get the job done for me,'' Civale said. ''I wasn't worried if he gave up a run or two - I just wanted the victory.''
Cleveland improved to 26-20 despite recent injuries to slugger Franmil Reyes and starter Zach Plesac. The latter was placed on the 10-day injured list Tuesday with a non-displaced fracture of his right thumb.
Tarik Skubal (2-6) took the loss despite a career-high nine strikeouts, allowing two runs, six hits and a walk in five innings. Detroit has lost four straight.
Cesar Hernandez hit Skubal's second pitch over the Cleveland bullpen in left field - the major league-leading 13th homer Skubal has allowed this season.
''That's a middle-middle fastball, and when you put a 92 mph fastball right there, that's what will happen,'' Skubal said. ''I can't do that.''
Cleveland had runners on second and third with no one out in the fourth. Owen Miller made it 2-0 with a groundout - his first major-league RBI - but Skubal escaped without further damage.
Detroit's best chance against Civale came after Badoo's two-out triple over center fielder Jordan Luplow's head in the seventh, but Castro flew out to left.
''He hit that a long way,'' Luplow said of Baddoo's triple. ''Playing center field here is being out on a football field.''
Luplow then gave Civale two insurance runs with a long homer to right-center field in the eighth.
''I've been able to do things to help us win a couple games here,'' said Luplow, who saved Monday's 6-5 victory with a diving catch in shallow right. ''I haven't been swinging well, but I'm finding ways to help.''
Francona said Plesac injured his thumb Sunday while ''rather aggressively taking off his undershirt'' after being knocked out of his start against the Minnesota Twins in the fourth inning.
The teams play the third of a four-game series on Wednesday evening, with Detroit's Jose Urena (2-4, 4.62) facing Triston McKenzie (1-3, 6.89). Francona said McKenzie - demoted to Triple-A over the weekend - will be optioned back to Columbus after the game.
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