BOSTON — Matt Moore picked a great time to pitch the first shutout and probably the best game of his two-year major league career.

The left-hander, making his first start since pitching in the All-Star Game, dazzled the Red Sox with a two-hitter and pitched Tampa Bay to within a half-game of Boston in the American League East with a 3-0 victory Monday night.

“I think that’s probably the best game I’ve ever thrown; taking into consideration the Red Sox are playing pretty well right now and we’re on the road,” Moore said after throwing 109 pitches in his first big-league complete game.

“It’s my first (complete game) and for it to be a shutout at 109 pitches or so, it feels very good to be able to play that clean a defense, put up a couple of runs and let the bullpen have a night (off).”

His manager, Joe Maddon, ranked this performance with the seven-inning, two-hit shutout Moore, then a rookie, threw at the Texas Rangers in Game 1 of the 2011 ALDS, when Moore went to the mound with nine innings of major league experience on his resume.

But this was a shutout. And it gave the rampaging Rays their sixth straight win, their 14th in the last 15 games, and their 18th in their last 20.

A month ago, the Rays were in last place in the division. Now, they’re even with the Red Sox in the loss column. And Moore, who became baseball’s first 14-game winner (Detroit’s Max Scherzer joined him later), has won six straight starts. He has allowed just 20 hits in 42 innings, striking out 44 in that stretch.

“This is what he’s capable of on any given night,” said pitching coach Jim Hickey.

Said Maddon, who got the complete game from Moore on a night closer Fernando Rodney was resting after pitching three straight days: “He was really good from the very first inning. I was just talking to Stan (bullpen coach Borowski). Stan said he didn’t warm up very well, either, that’s how this game works. Great command of all of his pitches tonight … primarily he pitched with (his) fastball and commanded his fastball.

“Just looked composed, in charge, emotions were in check — everything was just there tonight. We’ve been talking about once he gets command of his fastball, heads up.”

The win was only Tampa’s fourth in 13 games against the Red Sox this season, the Rays’ second in seven games at Fenway Park.

Moore, beating Boston for the second time this season, outdueled Red Sox rookie Brandon Workman (0-1), who yielded two runs in six innings in his second major-league start, both strong.

Moore gave up two singles and allowed only one runner as far as second base. During his six-start winning streak, he has allowed seven runs on just 20 hits.

“Overall, a very well-pitched game on both sides, but Matt Moore was the story of the night,” said Red Sox manager John Farrell.

James Loney, who became a new dad last Thursday night, drove in two runs, Desmond Jennings had a ninth-inning sacrifice fly and Ben Zobrist had three hits for the Rays.

Moore struck out four batters in a row in the second and third innings and didn’t strike anyone out the rest of the night. He walked only one.

Workman has yielded two runs in each start and still doesn’t have a win.

“He obviously threw the ball really well,” Workman said of Moore. “That was impressive to watch.”

Workman gave up a run but survived a 33-pitch first inning to work through six.

NOTES: Maddon, asked about the Ryan Braun suspension, said, “It’s obviously the right thing to do; and if more of that happens, based on good evidence, then I’m all for it.” On the other side, Red Sox RF Shane Victorino, a friend of Braun’s, said, “It’s a cloud for the game, especially when it’s one of the elite players of the game. People are going to say that’s why he’s elite, because he cheated. He’s still a good player, no matter what.” … Maddon said Rodney “is a tourist today” in declaring his closer out. Joel Peraltz warmed up lightly in the ninth, just in case. … Red Sox RHP Clay Buchholz got a positive report from Dr. James Andrews, who concurred on the diagnosis of bursitis in the pitcher’s right shoulder. Buchholz, who hasn’t pitched since June 8, can now return to Boston and resume his throwing regimen — flat ground, then three bullpen sessions and a simulated game before minor league rehab. … Tampa RF Wil Myers (wrist) sat out his second straight game and expects to play Tuesday. … RHP Roberto Hernandez starts for the Rays against Jon Lester (once 6-0, now 9-6) Tuesday. … C Jarrod Saltalamacchia, in a 1-for-19 slump with eight strikeouts, was out of the Boston lineup, as was SS Stephen Drew, who played his first two games off the disabled list Saturday and Sunday and went 0-for-5 with four strikeouts. … Daniel Paul Ruth-Hettrick, the great, great grandson of Babe Ruth, threw out the first pitch.