The Chicago Cubs were in prime position to end a horrible May on a positive note, threatening to send the Tampa Bay Rays to their first series sweep of the season.

With a day off Thursday before a 10-game West Coast trip, a win over the mighty Rays would’ve been reason to believe the Cubs’ prolonged stretch of bad baseball was behind them.

But a pair of late two-run homers off Mark Leiter Jr. gave the Rays a 4-3 comeback win in front of a sun-baked crowd of 29,360 at Wrigley Field, and an injury to Cubs starter Justin Steele made the day a total loss.

Steele was removed after three innings with left forearm tightness, a move the left-hander labeled precautionary.

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“I’m really not too concerned about it,” Steele said, adding his forearm was “throbbing” after the second inning. But he went out to pitch the third.

“Radar went way up, obviously,” manager David Ross said. “The trainers, they felt comfortable, and then watched him pumping the hand and stretching the forearm a little bit. Went out and checked on him (in the third). He said he didn’t feel it at all — no tingling or anything like that — so I let him finish.

“The more I watched him throw, the more nervous I got … so for precautionary reasons I pulled him.”

The Cubs need Steele in the rotation if they hope to contend, though no one seemed to believe the tightness would lead to a more serious issue.

“I think he’s all right,” left fielder Ian Happ said. “He did a good job. Have to be cautious with him. He’s really important for us and we need him the rest of the season.”

Steele held the Rays hitless through three innings, and the only hit off reliever Hayden Wesneski heading into the seventh was Manuel Margot’s fifth-inning grounder that shortstop Dansby Swanson bobbled before making a late throw to first.

Leading 2-0 in the seventh, Ross replaced Wesneski with Leiter to face the left-handed-hitting Brandon Lowe after a two-out walk.

“We had a mapped-out plan,” Ross said. “He had given us what we needed. I thought he threw the ball great. His strength is against righties, and Leiter’s is against lefties.

“Trying to match up strength on strength, knowing we’ve only got 2⅓ innings to cover. He hung a split to Lowe that ended up in the jet stream.”

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Lowe’s two-run blast tied the game at 2-2. After Trey Mancini’s pinch RBI single in the bottom of the inning gave the Cubs the lead again, Ross sent Leiter back out for the eighth.

Leiter walked leadoff hitter Taylor Walls and went 2-0 on Jose Siri, prompting a mound visit from pitching coach Tommy Hottovy.

Two pitches later, Siri cranked another two-run homer to center, putting the Rays up 4-3.

The Cubs had the tying run on third with one out in the eighth when ex-Cub Jason Adam struck out Swanson on a changeup. After a stolen base put the tying and go-ahead runs in scoring position, Adam fell behind Happ 3-0 before catching him looking at a sweeper for a called third strike.

Happ was already on his way to first and was shocked by the call. After looking at the video, he was adamant he drew a walk.

“It was a ball,” Happ said. “I can see that corner really well.”

The Cubs loaded the bases in the ninth with one out but again couldn’t score. Jalen Beeks struck out Miles Mastrobuoni before Yan Gomes lined a shot to left on a 3-2 pitch that Randy Arozarena ran down to end the game.

“I thought he was going to walk us off there in his 1,000th game,” Ross said of Gomes. “They were playing in the right position.”

The Cubs (24-31) finished May with a 10-18 record and are five games behind the division-leading Milwaukee Brewers.

“Three weeks or almost a month of good baseball, and this last month was not our best,” Ross said. “So it’s like, OK, let’s try to start this new month off the right way and try to play our best baseball.

“Mentally I stay day to day and don’t look ahead. But turning the chapter on this month kind of feels nice. I’ve got to give my dog her heartworm pill.”

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The health of Ross’ dog aside, the Cubs enter June with a new set of challenges and a better understanding of what they need to improve to get to the postseason, a goal that seemed plausible in late April.

A year ago the Cubs were 20-29 entering June and 11 games out of first. A 10-game losing streak that began June 4 put them out of their misery and made the final three-plus months irrelevant to anything but auditioning players for 2023.

Even if the Cubs manage to contend into July in a bad division, President Jed Hoyer might have to swallow hard and deal some of his assets to build for the future.

“Like I tell the boys, we just have to try to (avoid) those big losing streaks,” reliever Adbert Alzolay said. “I feel like the last two years, that’s the thing that’s been affecting us. After playing a really good month and then going two weeks losing games by one run, you see things start shifting a little bit.

“It’s keeping the same energy from the get-go. We have a great group of guys in this locker room and I feel like we have the talent to compete. As a team we haven’t been on the same page every day, hitting or pitching (at the same time). It’s part of building this new chemistry we have with all the new players we have here. I feel like we’re close to where we’re supposed to be.”

Closer, perhaps.

But still not where they should be two months into the season.