The team everyone loves to hate is alive for one more day — and its most outspoken player is a huge reason why.

Carlos Correa’s game-winning homer with one out in the bottom of the ninth off Nick Anderson gave the Astros a 4-3 win over Tampa Bay in Game 5 of the ALCS on Thursday at Petco Park in San Diego.

The shot, to dead center, leaves Houston down 3-2 in the series, as the Astros try to do something no team has done since the Red Sox won four straight in the 2004 ALCS to knock off the Yankees.

The Astros are halfway to completing the epic comeback — and they’re looking to perhaps the Yankees’ most painful defeat for inspiration.

Astros third baseman Alex Bregman showed Correa a portion of “Four Days In October,” ESPN’s documentary on Boston’s famous comeback against the Yankees, on Wednesday night and Correa said it got him excited for Thursday.

“It was a super-inspiring video,’’ Correa said. “[The Red Sox] are the only team that has been able to do it. We won two games now and there’s still a long way to go. We have to go out [Thursday] and take that game.”

Correa made sure they had that opportunity, with some flourish.

He called his shot to Houston manager Dusty Baker in the bottom of the ninth.

“Carlos told me before he went up there he was gonna hit a walk-off [homer],” Baker said. “I said, ‘Go ahead.’ ”

He drilled a fastball over the wall in center, setting off a celebration at home plate during which Correa said to Baker, “I f–king told you.”

Now the Astros will turn to Framber Valdez in Game 6, with the Rays going with Blake Snell in a game Tampa Bay had hoped to avoid after winning the first three games.

“They’ve got a little momentum on their side,” said Kevin Kiermaier, who saw Correa’s homer sail over his head as he leapt at the wall in center. “We’ve got a 3-2 lead. We have to get momentum going for us and create that early in the game and get our mojo back.”

The Rays seemed to have found their mojo after erasing a two-run deficit thanks to a solo homer from the sizzling Randy Arozarena in the fifth and another by Ji-Man Choi to lead off the eighth.

But they couldn’t get ahead, and Correa, who has seemingly embraced the fact fans don’t like the Astros thanks to the sign-stealing scheme they were found to have used on their way to the 2017 World Series title, came through.

Correa, who mocked fans still angry about the cheating scandal after Houston beat the Twins in the AL Wild Card Series, had an impromptu lesson with hitting coach Alex Cintron after Correa’s second at-bat and made a subtle adjustment to his swing.

His next time up, Correa lined out to second before he came up again with one out in the ninth.

“Anderson is a great pitcher,’’ Correa said. “I don’t mean [any] disrespect when I called my shot.’’

And it came just in time for Baker, who had Valdez up in the bullpen to come into the game if it went into the 10th inning, which would have left him unable to start Friday.

As good as the Astros feel after the last two games, Baker acknowledged they have their work cut out for them.

“The pressure is still on us,’’ Baker said. “We’ve got to win two [more]. This team has done well and flourished under pressure. Only a few teams have come back from [down] 0-3. We’d like to join that few … Hopefully it will go down as one of the greatest comebacks in history after two more games.”