BOSTON -- Fresh from an off-day shopping spree at the neighborhood Target to stock his new house, rookie manager Alex Cora showed up for work Thursday and offered a candid assessment of the first-place Boston Red Sox after the season’s first week.

“The good thing,” Cora said, “is we haven’t played our best baseball.”

Over the next few hours, in the 107th annual opening of Fenway Park, the Red Sox lived up to that evaluation. They barely hit for eight innings against a Tampa Bay Rays pitcher who was making his first career start before their bats finally awakened in the ninth. They ran into another out in the first inning and failed to score after a leadoff triple in the second. A relief pitcher faltered in the eighth inning after the starter went seven scoreless. The new $110 million cleanup hitter recorded two hits but remained homer-less and grounded into a double play with a chance to win the game in the ninth inning.

It was a performance as imperfect as the conditions -- sunny, but 40 degrees with an 18-mph wind at first pitch.

But the Red Sox won. Again. Warts and all, they came back to defeat the Rays 3-2 on Hanley Ramirez's bases-loaded single over the head of right fielder Carlos Gomez in the 12th inning.

Never mind that they have made seven unforced outs on the bases in seven games. Or that aforementioned slugger J.D. Martinez has two extra-base hits in 27 plate appearances. Or that the bullpen ERA is 4.00. The surging Sox have won six games in a row since a late-game gut punch on Opening Day at Tropicana Field and are tied with the World Series champion Houston Astros for the best record in the American League.

“We’ve been finding a way to do it,” star right fielder Mookie Betts said. “Haven’t scored a whole lot of runs, but we’ve found ways to manufacture some. Obviously the pitcher has been what’s kept us in every game.”

It helps, of course, that the first seven games have been against the Rays and Miami Marlins. Nothing against the Florida baseball teams, but neither are very good. A two-time defending division champ with expectations of going back to the postseason should clean up against those clubs.

But it’s true, too, that Martinez is bound to find his power stroke. Signed to replace David Ortiz, who took part in the Fenway-opening festivities by meeting Olympic medalist Aly Raisman at the mound and revealing a “Girl Power” T-shirt, Martinez is still finding his timing after a shorter-than-usual spring training. Moreover, No. 2 hitter Andrew Benintendi will overcome a slow start (4-for-23, no extra-base hits), and the offense, in general, will heat up along with the weather.

And when that happens, well, buckle up.

“We have to improve in a few aspects, baserunning [being] one of them,” Cora said. “But pitching and defense have been solid. The at-bats are getting better. People can say it’s early, but it’s always good to have a good start, so we’ll take it as it is.”

While the Red Sox round the rest of their game into shape, the starting rotation is dealing. For the second consecutive start, David Price blanked the Rays for seven innings and became the first Red Sox pitcher since Mel Parnell in 1949 to spin at least seven scoreless innings in consecutive starts to open a season.

Between them, ace lefty Chris Sale, Price, Rick Porcello and fill-in starters Hector Velazquez and Brian Johnson have allowed four earned runs in 42 innings for a 0.86 ERA. The Red Sox are the first team in major league history to have their starters allow one run or less in each of a season’s first seven games.

If not for Cora’s forward-thinking desire to limit the starters’ workload early in the season in an attempt to keep them fresh later, the numbers might be even more dazzling.

“It was huge to go out there and get 21 outs and give up no runs,” Price said. “I didn't know if I was going to go back out for the eighth, but if I would’ve been sure, I definitely would’ve tipped my cap [to the fans]. But I didn’t want to show Alex that I thought I was going to come out.”

By then, the sellout crowd likely was too frozen to clap anyway. And the hearty souls who stuck around for the ninth inning were rewarded with a game-tying rally. Ramirez singled home Betts, and after Martinez hit into a double play, Xander Bogaerts lined an RBI double off the Green Monster against Rays closer Alex Colome.

In the 12th inning, after unheralded rookie lefty Bobby Poyner tossed two scoreless frames, Ramirez won the game and raced around shallow right field to escape joyous teammates who wanted to douse him with water.

“I don’t want that. It was too cold,” Ramirez said. “That warmed me up a little, that sprint right there. When you win, anything is fine.”

And the Red Sox have been winning, even though they aren’t playing their best. Consider it proof of how good they really are.