ST. PETERSBURG -- On getaway night, the Tigers couldn’t find a way to close out a sweep of the Rays. Instead, following a 7-5 defeat on Wednesday at Tropicana Field, Detroit was consoled by winning the road series and getting a much-needed off-day after a rigorous 14-day stretch.

“We’re going to get on a plane … we’re going to go home, and we’re happy with the road trip,’’ Tigers manager A.J. Hinch said. “You want to get greedy when you have the chance to sweep them, especially when we had the lead in the middle part of the game. But [the Rays] came up bigger in the big moments.’’

No moment was bigger than the sixth inning when the Rays rallied against reliever Will Vest, who had been enjoying a dominant April. But with the Tigers leading, 5-4, Vest surrendered a game-tying two-out single to Ben Rortvedt.

Tampa Bay second baseman Curtis Mead, who didn’t have an extra-base hit in 64 at-bats, then picked on Vest’s 2-2 slider and lifted it over the short fence in the Trop’s left-field corner for a 327-foot home run (his second MLB homer).

After getting to 2-2, Mead fouled off three consecutive pitches before getting a slider up in the zone.

“That’s the competition. … The ballpark obviously gave them a big boost after we had just taken the lead,’’ Hinch said.

“I mean, [Vest] left it up,’’ Tigers catcher Jake Rogers said. “But all these hitters over there, they’re good hitters. They’re all big league hitters. They all got here for a reason. [Mead] did what he’s supposed to do with it.’’

Detroit starter Jack Flaherty assumed some of the blame. He was lifted after the fifth inning because his pitch count reached 97. Unacceptable, he said.

“I’ve got to do a better job … the game is on me,’’ Flaherty said. “That’s what happens when you go five. Vest has been unbelievable all year [1.64 ERA in the previous 10 appearances], and he has continued to throw the ball well, but I’ve got to go deeper. Going five just doesn’t get the job done.

“I’ve got to be out there for the sixth. So that’s on me.’’

After two innings, the Tigers trailed, 4-1, and had the uncomfortable prospect of facing their former teammate, left-hander Tyler Alexander, who pitched four innings in a bulk role following opener Shawn Armstrong. Hinch compared it to “playing against a relative or a brother,’’ but Detroit closed the deficit to 4-3 on Mark Canha’s two-out, two-run single in the fifth.

The Tigers scored two more in the sixth against righty Chris Devenski to surge ahead 5-4. Matt Vierling began the rally with a one-out triple to the right-field corner, then scored on Buddy Kennedy’s single. After Kennedy stole second, Javier Báez delivered a full-count RBI double and the Tigers led.

Not for long.

But Detroit focused on the long-term silver lining.

“We want to win as many as we can, and obviously, getting the win in this series against this ball club is good,’’ Rogers said. “You know, the boys are winning. We want to win a little more.

“We’re taking the wins when we can. Hopefully, we can keep going forward against the next teams that are coming to Detroit [Friday begins a homestand against the Royals and Cardinals] and get a couple more there.’’