Garrett Mitchell homered, the Milwaukee bullpen provided 3 2/3 innings of shutout relief and the Brewers held on for a 3-2 road victory over the San Francisco Giants in the opener of a three-game series Tuesday night.

The Brewers (83-61) took another step toward a National League Central championship, while the Giants (71-74) fell eight games out of the NL’s final wild-card spot with just 17 to play.

In the opener of a six-game trip, the Brewers led just 2-1 entering the sixth inning, when Mitchell launched reliever Tristan Beck’s first pitch for his fifth home run of the season.

Mike Yastrzemski got the Giants back within 3-2 when he smacked a leadoff homer of his own in the bottom of the inning, his 14th.

Brewers starter Aaron Civale (6-8) then retired Heliot Ramos on a pop fly before turning the ball over to the Milwaukee bullpen, having allowed two runs and three hits in 5 1/3 innings. He walked one and struck out two.

DL Hall retained the one-run lead through the seventh inning. Trevor Megill worked a 1-2-3 eighth before Devin Williams struck out Tyler Fitzgerald with two aboard in the ninth for his 10th save.

In the first inning, Milwaukee took a lead it never relinquished.

A leadoff double by Jackson Chourio ignited a two-run first by the Brewers. William Contreras and Willy Adames drove in the runs with singles off Giants starter Landen Roupp (0-1).

The Giants responded in the last of the inning, getting a two-out RBI double from Matt Chapman.

Roupp worked the first five innings for San Francisco, limiting the Brewers to two runs and five hits. He struck out three without issuing a walk.

Contreras collected three singles and Adames had a pair for the Brewers, who took two of three from the Giants in Milwaukee last month.

The Brewers out-hit the hosts 9-4.