Milwaukee (84-73) remained a half-game back of the Phillies for the third NL wild-card spot. Philadelphia snapped a five-game losing streak earlier in the day with a victory over the Nationals in Washington.
Burnes (12-8) allowed four hits and lowered his ERA to 2.98.
''That's what great players do,'' Brewers manager Craig Counsell said. ''They step up and give you great performances when you need them most. That's exactly what Corbin did tonight. Not only was it eight dominant innings, but it helps us out a ton going into the weekend.''
Devin Williams struck out three and worked around a pair of walks in the ninth for his 15th save.
Alcantara (14-9) struck out eight over his eight innings and held Milwaukee to five hits, two by rookie center fielder Garrett Mitchell.
Mitchell led off the sixth with a base hit up the middle, then stole second and moved to third on Willy Adames' single before scoring the game's only run on Rowdy Tellez's sacrifice fly to the track in center.
''I went to a two-strike approach right away and made sure (I made contact),'' Tellez said. ''I didn't worry about hitting the ball hard, I just wanted to hit it deep enough. We've got Mitch on third, so he can run. That was it, just put something in the air.''
Miami didn't put a runner into scoring position until the ninth, when Lewin Diaz led off with a single and Jon Berti drew a five-pitch walk off Williams.
Williams struck out Miami's next two batters, bringing up former teammate Avisail Garcia, whose grand slam a night earlier dealt Milwaukee a loss. Garcia walked on four pitches, loading the bases but Williams recovered, striking out Jesus Sanchez to end it.
''Burnes just doesn't give in,'' Marlins manager Don Mattingly said. ''He doesn't throw anything on the plate, everything is on the edge with him. Guys don't really get anything to hit or you have to really work to get something to hit. He just doesn't give in. He's really good.
''We finally got something going in the ninth and had a couple of chances, we just weren't able to get that hit.''
Alcantara became the first pitcher in Marlins history to strike out 200 batters in consecutive seasons when he whiffed Milwaukee's leadoff batter, Christian Yelich, in the first inning.
He set a career high with 201 strikeouts last season and surpassed that mark in the third against Mitchell while also moving into a tie with Ryan Dempster for sixth on the Marlins' career strikeout list with 628.
''Last year, we thought he was pretty good but he keeps getting better,'' Mattingly said. ''The bar's pretty high and he keeps setting it higher.''
Burnes, meanwhile, increased his total to 238 strikeouts for the season to surpass his previous career high of 234, set a year ago. He leads the NL and is second only to the Yankees' Gerrit Cole (248) in the majors.
After winning the NL Cy Young Award last season, Burnes said Alcantara is more than deserving of the honor this time around.
''What he's done as far as going deep into games, doing it start in and start out, he goes out there and gives them seven, eight or nine innings and gives them a chance to win,'' Burnes said. ''Obviously, they're not the best baseball team this year which makes it even tougher to go out there and do what he's doing so yeah, he would be my Cy Young this year.''
Marlins: SS Miguel Rojas returned to the starting lineup Friday after sitting out the last two games with a sore wrist.
The series continues Saturday with Marlins right-hander Edward Cabrera (6-4, 3.15 ERA) facing off against Milwaukee left-hander Aaron Ashby (2-10, 4.50 ERA).
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