CINCINNATI — Five solo homers. No surprise that Rod Barajas hit the one that made all the difference.

Barajas hit a tiebreaking solo shot in the ninth inning Tuesday night, rallying the New York Mets to a 5-4 victory after the Cincinnati Reds had caught up with a couple homers of their own, the last one upheld after a review.

There was no doubt about the one that Barajas hit off Reds closer Francisco Cordero (1-2), who left his first pitch to his former teammate in a very bad place.

“We played in Texas together (from 2004-06), and I know he’s got a lot of pop,” Cordero said. “I lost the game. It was a little mistake.”

Barajas’ seventh homer decided a game full of them — two by the Mets, three by the Reds. The catcher has homered five times in the last nine games, and seems to hit them at the right time. Four of the homers have either tied the score or put the Mets ahead.

“He’s been impressive in that manner,” manager Jerry Manuel said. “He’s had some big hits at some big moments.”

The Mets blew a 4-2 lead in the eighth when Joey Votto and Scott Rolen hit back-to-back homers off Fernando Nieve. Rolen’s homer was upheld by an umpire’s review — the ball cleared the wall before a fan touched it.

Pedro Feliciano (1-0) got the final out in the eighth. Francisco Rodriguez pitched a perfect ninth for his fourth save in five tries, ending the Mets’ three-game losing streak.

New York has struggled to win tight games, going 3-5 in those decided by one run.

“It’s good to win a close game,” said David Wright, who hit the other solo homer. “That’s something we have not been able to do a lot of this year. Hopefully this gives us a little momentum.”

Votto had two of Cincinnati’s six hits, including a solo homer with two outs in the eighth off Nieve that cut it to 4-3. Three pitches later, Rolen hit a drive to center. Angel Pagan jumped, but couldn’t reach it. A man in a Reds shirt reached up and touched the ball after it cleared Pagan’s glove.

Manuel came out of the dugout to argue for interference. Plate umpire Tim Welke — also the crew chief — needed only 1 minute, 45 seconds in the replay area to uphold the call.

That’s the way it’s gone lately for the Mets, who have spent much of the season trying to overcome a slumping offense. New York did a last-to-first surge by winning eight in a row, relying on its rotation to make headway in the NL East. Then, the Mets lost three straight.

The offense came through, ending the slide.

“You don’t want to be a team that diminishes a winning streak with a bad streak,” Manuel said. “You want to right the ship.”

Wright homered in the fourth off Bronson Arroyo, who gave up four runs in seven innings. Jose Reyes had a run-scoring single in the first and a double in the sixth inning, the key hit in a two-run rally that made it 4-2.

At that point, right-hander John Maine was in position for his first career win over the Reds. He had lost all three of his previous career starts against Cincinnati, getting roughed up by homers.

He gave up one this time — Brandon Phillips’ solo shot that smacked off the left-field foul pole in the first inning. A throwing error let in an unearned run off Maine, who gave up four hits in six innings.

For once, the Mets managed to string a few hits together.

Pagan, Luis Castillo and Reyes opened with consecutive singles off Arroyo for a 1-0 lead. Arroyo induced a double-play grounder by Wright to end the rally. In his next at-bat, Wright hit his sixth homer into the upper deck in left field, extending his hitting streak to eight games and helping the Mets keep pace in the home run splurge.

“I don’t think we need to hit a lot of them to be successful, just one here or there,” Wright said.

NOTES: Mets RHP Mike Pelfrey is still expected to make his scheduled start Friday in New York against the Giants. He had a precautionary MRI after feeling stiffness in the shoulder his last time out. The Mets have told him to ease up during his between-starts workout in the bullpen. … Gary Matthews Jr. pinch hit and grounded out, leaving him in an 0-for-15 rut. Since April 7, he’s 3 for 35 with 14 strikeouts. … Welke took Drew Stubbs’ foul ball directly off his facemask in the fifth inning. Welke removed his mask and walked around home plate before settling back in.