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ST. PETERSBURG, Fla. — Alex Cora­ slept peacefully through the night before his first game as a major league manager on Thursday. Instead of rushing off to the ballpark in the morning, he ran a quick errand to pick up diapers and baby food for his 8-month-old twin boys.

“It’s just a regular game, man. For me, this is something I always wanted to do, but it’s not going to change who I am,’’ Cora said.

That could depend on his bullpen. A near-perfect day turned into a disaster for Cora and the Red Sox when the Tampa Bay Rays scored six runs in the eighth inning to claim a 6-4 victory.

Joe Kelly and Carson Smith could have used diapers. They combined to give up four walks and three hits to a lineup that had been shut down the previous seven innings.

“It’s pretty pathetic what I did,’’ Kelly said. “You can’t do that.’’

It took one game for Cora’s strategy to come under scrutiny. His honeymoon ended on the church steps.

The Sox had a 4-0 lead after seven innings. Chris Sale allowed one hit over the first six and struck out nine. Matt Barnes then worked a perfect seventh. Sox pitching had retired 15 of the last 16 batters to that point.

Cora had several options open at that point and went to Kelly because the matchups favored his fastball. The righthander walked leadoff hitter Daniel Robertson but came back to strike out Rob Refsnyder.

Kelly got ahead of Matt Duffy, 0 and 2, and missed twice. His next pitch was a slider right over the plate that Duffy lined to right field for an RBI double.

Kelly walked Kevin Kiermaier and Carlos Gomez to load the bases. It was only the second time in 99 career relief appearances Kelly had three walks.

When Smith came in, he walked Brad Miller on five pitches to force in a run.

“Walking the first guy, can’t do that,’’ Smith said. “Put my back up against the wall.’’

Smith struck out Wilson Ramos and got ahead of Denard Span, 1 and 2. One pitch away from ending the inning and holding the lead, Smith couldn’t put Span away.

Span fouled off a full-count pitch then lined a triple to right field.

Adeiny Hechavarria followed with an RBI infield single.

The Sox did not blow a lead of more than three runs all last season. That left Cora having to explain what he did and didn’t do.

He did not use Craig Kimbrel in the eighth inning, a decision made before the game. Kimbrel pitched only twice in spring training after spending three weeks in Boston when his infant daughter had heart surgery.

“We’re not going to put him in that spot right now,’’ Cora said. “We feel he’s ready but I don’t think it’s fair for him to come into that situation, it’s not a clean inning.’’

Cora said it would take a few weeks to build Kimbrel up to handle four or five outs given his abbreviated spring training. Had Smith held the lead, Kimbrel was coming in for the ninth.

“We have to take care of players and that’s the way we’re going to take care of him,’’ Cora said. “He’s ready to pitch. But we’re not going to jeopardize his health just because there’s traffic in the eighth inning.’’

Cora had a lefthander in the bullpen, but he didn’t want Bobby Poyner making his major league debut against Span with the bases loaded.

“Nah. We’re not going to put him in a spot like that,’’ the manager said.

A bigger issue is that the Sox traded for Addison Reed last July to improve the bullpen but let him walk as a free agent after the season and never replaced him.

President of baseball operations Dave Dombrowski said throughout spring training that the team had ample depth. Not Thursday.

It left Sale with no decision on a day he pitched with his usual ferocity.

“We show up to win,’’ Sale said. “Things like that happen.’’

Pitching for the first time since he was struck on the left hip by a line drive in his final start of spring training, Sale struck out nine and walked three over six innings. The Rays advanced only two runners beyond first base against him.

The Sox took a 3-0 lead on Rays starter Chris Archer in the second inning thanks to an unconventional home run.

J.D. Martinez drew a walk in his first plate appearance as a member of the team. Xander Bogaerts’s double to the gap in left sent Martinez to third. He scored when Rafael Devers grounded to shortstop.

Nunez then sent a shallow fly ball to the gap in left that Span and Kiermaier converged on. But Span hesitated then ducked away as Kiermaier approached and the ball fell between them.

Nunez rounded the bases as Kiermaier chased the ball down. New third base coach Carlos Febles, in his first big decision of the season, sent Nunez to the plate.

Robertson collected the relay throw just behind shortstop and had a play on Nunez. But his throw to the plate was straight into the back of the mound and bounced away.

Nunez slid across the plate on his stomach and signaled he was safe.

It was the first inside-the-park home run for a Sox player on Opening Day since Carl Yastrzemski in 1968 at Detroit.

The Sox added to their lead in the seventh inning when Bogaerts and Devers led off with doubles. But it didn’t last.

Cora watched plenty of meltdowns during his playing career. Were the emotions different as a manager?

“As a player I was upset and you turn the page and show up tomorrow,’’ he said. “As a manager, I’m upset. Turn the page and show up tomorrow.’’

Peter Abraham can be reached at peter.abraham@globe.com. Follow him on Twitter @peteabe.