ST. PETERSBURG, Fla. -- Stellar pitching is keeping the Milwaukee Brewers right on the Chicago Cubs' tail in the National League Central.

Zach Davies threw seven dominating innings of one-hit baseball and the Brewers shut out the Tampa Bay Rays for the second straight night, winning 3-0 on Saturday at Tropicana Field.

"Zach was really flawless. He was outstanding," Milwaukee manager Craig Counsell said after the Brewers got back-to-back road shutouts for the first time since 2010. "He got through seven innings in a really efficient way ... He pitched beautifully. He had four pitches working, four real weapons he can use to get outs with."

Hernan Perez hit a solo home run in the ninth for separation in what had been a 1-0 game, and Milwaukee (59-53) handcuffed Tampa Bay's hitters as it did in Friday's series opener. The Rays (57-55), held scoreless in their last 20 innings, were shut out in back-to-back games for the first time since April 2016, against the Indians and White Sox.

"Needless to say, the offense has gone a little bit quiet," Rays manager Kevin Cash said. "(Davies) had a feel for every single thing he threw out of his hand and made it challenging."

The Cubs also won Saturday, so the Brewers remain a half-game back of the division leaders.

Davies (13-5) took a no-hitter into the sixth inning, and when Lucas Duda finally broke through with a single. Davies immediately followed by getting Evan Longoria to ground into a double play.

The Rays had a runner at third with one out in the fifth after a throwing error by Perez, but catcher Jesus Sucre lined out to center to end the inning.

Rather than use closer Corey Knebel on back-to-back nights, Milwaukee had Anthony Swarzak pitch the ninth for his first save with the Brewers and his second this season.

The Rays had a chance in the eighth inning against reliever Jacob Barnes, with Adeiny Hechavarria leading off with a single and Sucre following with a one-out bloop single. A throwing error by catcher Manny Pina put runners at second and third with one out, but Corey Dickerson struck out.

"He made a huge pitch to get the strikeout right after it," Counsell said. "Dickerson's a hitter that is able to put his bat on a lot of balls. He got one down and nasty enough to get a swing and miss."

Duda was hit by a pitch to load the bases for Longoria, but he popped out to center field to end the inning.

The Rays spoiled a quality start by Alex Cobb (9-8), who pitched six innings, holding the Brewers to one run. Reliever Ryan Stanek had four strikeouts in the seventh and eighth, but stayed in too long, giving up the home run to Perez -- his 12th of the season.

Stanek then gave up a single and walk to put two on with no outs, but Jose Alvarado -- who struck out the side in nine pitches in the ninth Friday -- fanned Jonathan Villar and Orlando Arcia. He was a strike away from getting out of the inning, but his wild pitch allowed Aguilar to score to make it 3-0.

For the second night in a row, the Brewers held to a 1-0 lead in a pitchers' duel.

Davies allowed only one baserunner in the first four innings -- a second-inning walk to Brad Miller. Miller reached on an error in the fifth, and the Rays had runners at first and third after a walk, but Davies got Sucre to line out to center to end the inning.

Milwaukee's only run off Cobb came on an RBI double by Arcia in the third inning, scoring Keon Broxton, who had singled.

Milwaukee had five hits, but Cobb kept the Rays close, striking out six batters in the first five innings.

"Alex grinded his way through six innings, one run," Cash said. "That's funny to say, because you'll take that start any day of the week. Alex wasn't as sharp, but credit him a lot for keeping it right there. We just couldn't get the big hit."

Brewers third baseman Travis Shaw, who leads the team with 74 RBIs, had to leave Saturday's game after he was hit in the side of the neck by a throw from home as he tried to steal second base.

Shaw stole second base, but Sucre's throw knocked his helmet off as he slid into the base. Shortstop Hechavarria's glove also hit him in the side of the face as the throw came in. Shaw stayed down for several minutes as trainers attended to him. He walked off the field slowly but on his own, and was replaced by Perez, who pinch-ran for him and took over at third base.

Counsell said that tests were all clear for Shaw, who has a neck contusion, feeling a little stiff and is considered day-to-day.

NOTES: Rays RHP Jake Odorizzi, on the disabled list since July 25 with a lower back strain, will be activated and rejoin the rotation to start Wednesday when the Rays face the Red Sox. ... Rays rookie RHP Austin Pruitt, who picked up the win in Wednesday's shutout victory against the Astros, will start Tuesday's game against Boston. ... Brewers RHP Brandon Woodruff, who won in Friday's series opener, became the 19th pitcher in franchise history to win in his major league debut, and just the fifth Brewer to throw a scoreless start in his debut. The last? Chris Saenz in 2004. ... Counting Saturday's game, the Brewers have played the Rays only 11 times, the fewest times Milwaukee has faced any major league team.