CINCINNATI — The Mets batted out of order in the first inning Wednesday against the Reds — and lost a runner in scoring position because of it.

The lineup card that first-base coach Ruben Amaro Jr. handed to the umpires before first pitch had Asdrubal Cabrera second and Wilmer Flores third. But the version the Mets released publicly — and the version they followed in the first inning — had Flores second and Cabrera third.

Interim manager Jim Riggleman and the Reds bench played it well. When Flores stepped to the plate, they said nothing. Flores struck out swinging.

When Cabrera stepped to the plate, the Reds still said nothing. Cabrera blooped a double down the left-field line. That’s when the Reds brought the inaccurate order to the attention of home-plate umpire Gabe Morales, who charged the Mets with an out, ending the inning and leading to official scoring chaos.

Cabrera’s double was changed to a putout to catcher Tony Cruz, then changed back to a double, then changed to nothing at all, leaving Cabrera 0-for-0 with no official at-bat.

Cleanup hitter Jay Bruce, who had nothing to do with anything other than stepping to the plate to hit after Cabrera, was charged with the penalty for batting out of order (the putout to the catcher).

No. 5 hitter Adrian Gonzalez led off the second inning and singled.

After batting out of order, the Mets had to stick with the lineup the umpires received pregame: Cabrera second, Flores third. Manager Mickey Callaway checked with Morales before their spots came up again to make sure.

The Mets went on to lose the game in 10 innings, 2-1.

After the game, Callaway took responsibility for the Mets batting out of order, but didn’t say he’s the one who fills out the card.

Said Callaway: “It probably cost us the game.”