It was Haase's fifth home run of the season and his second in the last three games. Miguel Cabrera also drove in a run for the Tigers, who improved their league-worst road record to 11-23 and split the two-game series.
''Definitely looking slider,'' Haase said. ''Fortunately for me, I got one in the zone and just something I could handle.''
Added Tigers manager A.J. Hinch: ''I loved how he handled the game behind the plate and also came up big with the homer when we needed it to separate us a little bit and give us a little breathing room.''
Rony Garcia (3-2) won his third consecutive start for Detroit, allowing one run on four hits with four strikeouts in five innings. Gregory Soto pitched a perfect ninth for his 15th save in 17 opportunities.
''It was wonderful,'' Garcia said through a translator. ''It was very, very good. I tried to do the job and fortunately, we were able to win the game today.''
Evan Longoria had a first-inning home run for the Giants, his eighth of the year, but San Francisco couldn't capitalize on late-inning chances to tie the game.
Down 3-1 in the seventh, the Giants loaded the bases with one out. Mike Yastrzemski grounded into a fielder's choice, allowing Tommy La Stella to score and cut the deficit to one. After a walk to Longoria loaded the bases again, Austin Slater struck out on three pitches.
In the eighth, La Stella doubled to left with two outs, but Wilmer Flores grounded out to third to end the inning. Overall, the Giants left nine runners on base.
San Francisco starter Alex Wood (5-7) fanned six in 5 2/3 innings but surrendered three runs on seven hits to take the loss.
''These are the days that are just extremely frustrating,'' Wood said. ''I felt really good. I thought it was the best my slider's been in a long time, if not (all) year. So to have that (home run) happen at the end really sucked, to be honest. Just really frustrating.''
Tigers: RHP Michael Pineda (fractured right middle finger) is expected to come off the injured list and start Friday against Kansas City. ''We're not gonna make anything official until likely Friday morning,'' Hinch said. ''He's penciled in. That's about as far as we need to take it.''
Giants: OF LaMonte Wade Jr. returned after missing nearly six weeks with left knee inflammation. Wade led off and went 1 for 5. ... LHP Jose Alvarez (lower back tightness) began a rehab assignment with Triple-A Sacramento on Tuesday, pitching a scoreless inning with one strikeout. ''He's gonna be off today and re-evaluated but it went well so far,'' manager Gabe Kapler said. ... RHP Jakob Junis (left hamstring strain) threw a bullpen session Tuesday.
The Giants optioned IF/C Yermin Mercedes to Triple-A Sacramento to make room for Wade on the active roster.
Tigers: Pineda (1-2, 3.22 ERA) is expected to come off the IL and open a three-game home series against the Kansas City Royals on Friday. Pineda hasn't appeared in a game since May 14. Brad Keller (2-9, 4.56) is slated to pitch for KC.
Giants: RHP Alex Cobb (3-3, 5.48) takes the hill Friday as San Francisco welcomes the Chicago White Sox for a three-game series. Lance Lynn (1-1, 6.19) will pitch for Chicago.
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