NEW YORK — Eager for a sliver of run support, Johan Santana found a clever solution.

He provided his own.

Santana lined his first major league homer and that was plenty as he pitched a three-hit shutout and led the New York Mets past the Cincinnati Reds 3-0 on a blazing Tuesday night.

Santana’s solo shot in the third inning drew a huge cheer from the baked crowd and an even bigger reception from his teammates.

“They said it was enough, that was all I needed for the game,” he said.

On a day when it hit a record 103 degrees in the city, Santana steamed around the bases after capping a tenacious 12-pitch at-bat with his drive off the right-field foul screen.

Santana took off his batting helmet, saluted the crowd with his right hand and came out for a curtain call to acknowledge the ovation. He became the second Mets pitcher to homer while throwing a shutout, joining Pete Falcone, who did it in 1981.

The Mets ace made the early edge stand up, shutting down the team that led the NL in runs, homers and hitting. He struck out five and walked three in his seventh career shutout and first since 2008.

Santana (6-5) had won just once in his last seven starts, though Mets hitters shared the blame. The left-hander ranked among the bottom among big league pitchers in backing, evidenced by New York scoring only one run in his previous three outings.

Santana drew another cheer the next time up as the video board replayed the highlight — the first home run in 182 career at-bats for a lifetime .166 hitter. The only other homer he remembered hitting, he said, came “in video games.”

“I hit it and started running,” he said. “I didn’t believe it was out.”

Santana wound up with the souvenir ball, proof that he’d accomplished what all pitchers often wish for.

“I’m on the board,” he said. “At least I hit one.”

The NL Central-leading Reds lost for the second time in seven games.

It was still 96 degrees when Brandon Phillips led off the game with a double. Putting aside worries that he was tipping his pitches, Santana didn’t allow another hit until Orlando Cabrera singled in the sixth.

The Reds threatened in the ninth when Scott Rolen singled with one out and left fielder Jason Bay dropped Jay Bruce’s flyball for an error. Mets manager Jerry Manuel strolled to the mound and, as fans implored him to leave in Santana, he did.

What did Santana tell Manuel? “I’ll finish it. Simple.”

Santana rewarded his manager when he got Jonny Gomes on a lineout and Drew Stubbs grounded into a game-ending force. Santana matched the best low-hit game of his career.

“You guys are trying to get me to say that he was something special tonight,” Reds star Joey Votto said. “But frankly, what I saw was the same guy we always see. He just missed a few more barrels.”

Matt Maloney (0-1) lost in his first game for Cincinnati this season. He traveled in from Triple-A Louisville earlier in the day, promoted because the Reds put pitcher Aaron Harang on the disabled list with lower back spasms.

Maloney retired the first seven batters. After rookie Ruben Tejada singled but was caught stealing, Santana stepped up. He took a ball from the Reds lefty, then fouled off the next seven pitches. After a ball and two more fouls, Santana took another meaty cut and pulled a drive that hit halfway up the foul screen.

“He had some good swings,” Maloney said. “I don’t have much experience with pitchers who can swing the bat. It worked out for him. Twelve pitches? I threw him everything I had.”

Jose Reyes returned to the Mets lineup after missing a week because of tightness in his lower back. A week before he goes to the All-Star game, the speedy Reyes beat out an infield single, and later had a bunt hit that helped set up Bay’s two-run single in the sixth.

The heat took its toll on the players and fans. Not every Mets player was on the field for batting practice and the Reds did their pregame stretching in an indoor batting cage.

Extra emergency personnel were on duty and bags of ice were available at all fan assistance centers. Even so, many fans left early because of the weather.

NOTES: Santana’s last shutout was Sept. 27, 2008, against Florida. He pitched his first complete game of the season and 10th of his career. … John Maine was the last Mets pitcher to hit a home run. He did it on July 24, 2007. … Bay’s error ended a string of 263 games without a mistake. … Santana is 4-0 lifetime vs. the Reds.