PHOENIX -- Zack Greinke is hitting his stride, and the Arizona Diamondbacks have the stopper they bargained for in the offseason.

The right-hander threw his first shutout since 2013 and did not permit a runner to reach second base in Arizona's 5-0 victory over the Tampa Bay Rays on Tuesday at Chase Field.

Greinke gave up three singles and walked two in his fourth consecutive win.

"That's him," Arizona third baseman Jake Lamb said. "That was the best I've seen him."

Lamb hit a three-run homer in the fourth inning off left-hander Matt Moore (2-4) and Paul Goldschmidt hit a two-run homer in the sixth to give Greinke plenty of cushion.

Greinke (8-3) struck out two and needed only 104 pitches. Tampa Bay had only one runner after Hank Conger's single in the fifth inning, a two-out walk by Corey Dickerson in the seventh.

Greinke got 14 ground ball outs, and the only particularly hard hit ball was Desmond Jennings' line drive single to center field with two outs in the first inning. Greinke extended his streak of scoreless innings to 16, dropping his ERA to a season-low 3.84.

"They put a lot of balls in play," Greinke said. "They hit some hard, some not as hard. Everything was kind of working right, or how you wanted them to, so you got a nice rhythm.

"You thought if you make a decent pitch, but if they put it in play it is going to be at someone. That was kind of how it was happening."

Greinke recorded his 150th career victory, joining Bartolo Colon, CC Sabathia, John Lackey and Justin Verlander as the only active pitchers to reach that milestone. Five of Greinke's last six wins have come after Arizona losses.

Jennings, Logan Morrison and Conger had hits for the Rays (26-31), who had a four-game winning streak broken. Arizona (26-36) has won two of three.

"We got beat by a really good pitcher," Tampa Bay manager Kevin Cash said. "He was on, changing speeds, hitting his spots. We competed well. The guy was just on."

Greinke recorded his first shutout since July 13, 2013, when he gave up two hits and struck out nine in a 1-0 victory over Colorado while with the Los Angeles Dodgers.

He had several chances for a shutout last season, three times throwing eight scoreless innings before being removed. He had 94 pitches in one of those starts, 93 in another.

"With pitch counts and Kenley Jansen, one of the best closers of the game, it was hard to get a situation to have that happen," Greinke said.

Goldschmidt also doubled and singled, and Welington Castillo had two hits as the Diamondbacks (26-35) won their second in three games.

Goldschmidt doubled with one and took third on Welington Castillo's single in the fourth inning before Arizona manager Chip Hale was ejected for arguing a strikeout by Brandon Drury.

Lamb hit his 11th homer two pitches later, a ball that bounced off the top of the left field fence. It was his fourth homer against a lefty this season.

"It wasn't changing my plan," Lamb said. "I was still going to go up there and be aggressive. It's definitely nice to know he (Hale) is fighting for us."

Lamb has five homers in his last 38 at-bats.

Goldschmidt has reached base in 13 straight games, hitting .386 with three homers and 11 RBIs in that stretch.

Moore gave up seven hits and five runs in seven innings. He struck out three and walked one.

"The home run by Lamb, that stinks," Moore said. "He put a better swing on it than the pitch was. The one by Goldschmidt, it was just lying in there for him."

NOTES: Tampa Bay 3B Evan Longoria did not start for the first time this season Tuesday, breaking a streak of 159 straight starts, despite a 10-game hitting streak and five homers in his last five games. "I hate taking days off," Longoria said. Longoria, 4-for-22 against Arizona starter RHP Zack Greinke, is expected to be back in the lineup Wednesday. ... Tampa Bay 2B Logan Forsythe will begin a short rehab assignment at Triple-A Durham on Wednesday, Rays manager Kevin Cash said, and could rejoin the team early in a 10-game homestand that begins against Houston on Friday. ... Arizona CF/SS Chris Owings missed the past two games with a left foot injury and remains a candidate for the disabled list, manager Chip Hale said. ... Diamondbacks RHP Shelby Miller (index finger) is scheduled to make a rehab start for Class A Visalia on Thursday. Miller has been out since May 25.