SAN FRANCISCO -- Chris Stratton has simple plans for his 27th birthday on Tuesday. Maybe just a nice lunch with his wife and infant son.

As for his first present, the Giants rookie right-hander got exactly what he wanted from manager Bruce Bochy on Monday night: a secure spot in the San Francisco rotation moving forward.

Stratton combined with three relievers on a four-hitter Monday, delivering the Giants a 2-0 victory over the Milwaukee Brewers in the opener of a three-game series.

Brandon Crawford's RBI double highlighted a two-run fourth inning off Brewers starter Zach Davies, which was enough to hand the right-hander his first road loss of the season.

"It certainly was a quiet night," Brewers manager Craig Counsell said. "It's one night we didn't swing the bats."

The Brewers (65-61) fell 2 1/2 games behind the first-place Chicago Cubs in the National League Central and 3 1/2 games back of the Arizona Diamondbacks for the second NL wild-card spot.

Making just his fourth major league start, Stratton (2-2) limited the Brewers to four hits in six innings. He walked two and struck out one.

Combined with his 6 2/3 shutout innings against the Washington Nationals in his previous start, a game in which he struck out 10, Stratton extended his scoreless-innings streak to 12 2/3. It is the longest streak for a Giants rookie since Chris Heston had a 16 1/3-inning shutout stretch in July 2015.

"I just left all the strikeouts in Washington," he joked afterward. "(Reliever Matt) Cain said, 'I had as many strikeouts as you did' (in his one inning)."

Despite his solid effort at Washington on Aug. 13, Stratton didn't pitch at all last week.

He had 10 and seven days off between his earlier starts as well.

"For how we're using him, he's really handled it well," Bochy said. "We skip him (in the rotation), give him five to six days off ... It doesn't faze him."

With Johnny Cueto likely to rejoin the rotation from the disabled list at or near month's end, Bochy was asked where Stratton fit in.

"Oh, he's earned his spot," the manager said. "We have options. Maybe we'll go to a six-man (rotation)."

Right-handers Cain, Mark Melancon and closer Sam Dyson followed Stratton with a hitless and scoreless inning apiece. Dyson overcame a one-out walk and a two-out balk in the ninth to record his 11th save.

The shutout was the Giants' first at home this season. They had been the only team in the majors without one entering play Monday.

Davies (14-7), who had been 7-0 on the road this season, left for a pinch hitter after six innings. He allowed just the two fourth-inning runs and seven hits. He walked two and struck out five.

"It was a tough battle," he said. "Those games are going to happen. You're not always going to be perfect."

Jarrett Parker, Hunter Pence and Pablo Sandoval had two hits apiece for the Giants, who have won 10 of their past 11 home games against the Brewers.

San Francisco finished with nine hits.

All four Brewers hits were singles on a night they had hoped to give Counsell his 200th career managerial victory on his 47th birthday.

The Brewers were shut out for just the second time since June 13.

A great play by Milwaukee shortstop Orlando Arcia in the fourth inning almost prevented the Giants from scoring their runs.

After Parker walked to open the inning, Arcia dived to corral Pence's hard grounder up the middle and flipped quickly to second baseman Neil Walker for a force at second. However, in his haste to try for a double play, Walker dropped the toss while trying to barehand it, not getting any outs on the play.

Crawford followed with a chalk-raising double down the right field line, scoring Parker with the game's first run. Pence later scored on Nick Hundley's infield out.

"That leadoff walk ended up hurting him," Counsell said.

The closest the Brewers came to scoring was when Stephen Vogt made a dash for the plate while Arcia, after singling, was caught in a rundown between first and second in the fourth. Giants first baseman Ryder Jones' accurate throw got a sliding Vogt at the plate.

NOTES: Giants 3B Pablo Sandoval was hit in the left forearm by a RHP Carlos Torres pitch in the eighth inning and was removed from the game as a precautionary measure. The injury is not considered to be serious. ... After having a night to munch on C Buster Posey's accusation that Phillies RHP Hector Neris hit him intentionally with a pitch, Giants manager Bruce Bochy blurted before Monday's game: "I'll say it: (Neris) is an idiot." ... Posey was given the night off Monday. ... The Giants released OF Melvin Upton Jr., who was playing at Triple-A Sacramento (12 games, .244 average). ... Brewers manager Craig Counsell announced before the game that LHP Brent Suter (strained rotator cuff) will throw a bullpen session Wednesday. Suter is eligible to come off the 10-day disabled list Tuesday. ... Despite an overcast day in San Francisco and being advised not to do so, Counsell took a glance at the solar eclipse Monday. "You've got to take a risk every once in a while," he said.