Milwaukee (82-64) won three of the four games in the series.
Taylor came through at the most opportune times, with his first run-scoring double leveling the game in the fifth inning before his second provided the Brewers with an insurance run in the seventh.
Elvis Peguero, Abner Uribe, Joel Payamps and Devin Williams took care of the rest, keeping Miami (75-72) in check after Milwaukee starter Adrian Houser (6-4) allowed two runs on five hits in five innings.
Williams worked a 1-2-3 ninth inning to pick up his 34th save of the season.
Sal Frelick chipped in with an RBI single for the Brewers, who have won five of their last seven games.
Jake Burger had two hits and Jacob Stallings added a run-scoring single for the Marlins, who are now one game in back of the Diamondbacks for the third and final National League wild-card spot. Arizona was scheduled to play the New York Mets later Thursday.
Miami starter Eury Perez (5-5) gave up three runs on five hits in 4 2/3 innings. He struck out seven without issuing a walk.
After Stallings put Miami ahead 2-1 in the top of the fifth, the Brewers struck for two runs in the home half of the frame.
Taylor doubled home Andruw Monasterio before coming around to score on Frelick's single. Taylor was initially called out at home after a strong throw to the plate from right fielder Jesus Sanchez, but Milwaukee successfully challenged the call to grab the lead.
Luis Arraez opened the game with a double, advanced to third on Burger's one-out single and scored on Sanchez's sacrifice fly. Rowdy Tellez had a sacrifice fly of his own in the fourth to draw the Brewers even at 1-1.
Milwaukee now leads the Chicago Cubs by 4 1/2 games in the NL Central.
—Field Level Media