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The Mets offense and bullpen picked up Sean Manaea, who had one bad inning.

But they couldn’t overcome the one bad misplay.

The Mets escaped from a five-run hole and sent the game into extra innings, only for a Brett Baty throwing error to pave the way toward a 7-6, 10-inning loss to the Guardians on Monday in front of 37,886 fans whose emotions swung wildly.

“That’s a tough one there,” manager Carlos Mendoza said after the Mets (63-50) fell for a sixth time in their past seven, although this series-opener was unlike the other losses.

Manaea went five strong, scoreless innings before coming apart in a five-run sixth; Pete Alonso keyed a five-run rally and smoked home run No. 251, bringing him one behind Darryl Strawberry for the franchise record; and the bullpen was excellent before the Mets threw the game away.

In the 10th inning, with two on base and Ryan Helsley on the mound, Cleveland’s David Fry bunted toward third base. Baty fielded the fairly hard-struck bunt and tried for the force out at second — and a well-executed play would have secured the out.

But Baty’s throw, to the first-base side, deflected off Francisco Lindor’s glove and into the outfield to score the go-ahead run. Two batters later, Gabriel Arias lifted a sacrifice fly for the run that decided the game.

“I’ve just got to make a better throw,” said Baty, who did not second-guess the decision.

“Couldn’t play catch, and we threw the ball away,” said Mendoza, who watched Baty try to atone by stroking an RBI single in the bottom of the inning before Luis Torrens’ flyout sealed it.

On a night the Mets left 10 on base, there were several moments for the club to bemoan, perhaps most significantly in the ninth inning. After Edwin Díaz struck his way out of runner-on-third, none-out danger in the top of the inning, the Mets offense allowed Cleveland’s Cade Smith to escape, too.

Francisco Alvarez led off the frame with a single and was replaced by pinch-runner Tyrone Taylor, who chugged around the bases on a double down the right-field line from Lindor.

But with one out, Juan Soto up next and Nolan Jones cutting the ball off before it reached the wall, third base coach Mike Sarbaugh held Taylor at third — a decision that Mendoza approved of, even if it backfired because Carlos Santana bobbled the relay throw.

“You get Taylor thrown out on the play right there with Soto and Pete coming up, you don’t want to be second-guessing that decision,” Mendoza said. “But I thought it was 100 percent the right one.”

Even if it didn’t work: Soto was intentionally walked before Alonso struck out and Jeff McNeil lined out, the big hit and the run that put the Mets over the top too elusive to grasp.

Wasted was a stirring comeback on the back of the super-bullpen — Brooks Raley, Tyler Rogers, Reed Garrett, Díaz and Helsley combining for 4 ¹/₃ innings without an earned run — and on the back of Alonso, who carried an offense that seemed buried.

After Manaea surrendered five runs in the top of the sixth, the Mets offense — which had collected all of three singles in the first five innings against Cleveland’s Slade Cecconi — awoke in the bottom of the inning.

The Mets scratched two runners on (Lindor reaching on a third-strike wild pitch before Soto smoked a ground ball that second baseman Brayan Rocchio couldn’t handle), before Alonso cracked No. 251 for his career — Strawberry should savor his final days atop the Mets home run standings — to left-center to bring the Mets within two.

First the offense showed a pulse, and then it showed life.

In the eighth, the top of the order again went to work. Lindor and Soto came through with back-to-back singles before Alonso collected his fourth RBI with a single into left.

After McNeil’s single loaded the bases, Mark Vientos sent a sacrifice fly to center to tie the game.

But as became a theme, the Mets could not find the final hit they needed: With two on, Cedric Mullins was robbed by a diving Rocchio before Baty grounded out.

“For us to battle back and keep fighting, that’s a lot of good signs,” Alonso said after setting a season-high with four hits. “It’d be more frustrating if we didn’t do anything, if we just laid down right there.”