But in a game-breaking top of the 11th inning, the Indians did just that, scoring seven runs to deliver the Red Sox a disappointing 13-6 defeat.
Instead of going to Cleveland with a 2-0 lead in the best-of-seven series, Boston had to settle for a split.
"We've got a war in front of us," said Red Sox catcher Jason Varitek. "Obviously they don't back down, we don't back down. We've got to be ready to play Monday."
This was Boston's first loss in the 2007 postseason.
"It certainly didn't end like we wanted it to, but for the very most part, that was one of the most exciting games I've ever been a part of -- so much good baseball," said Red Sox manager Terry Francona. "[It] just didn't end very well for us."
Pardon the Fenway faithful for not cheering one of their erstwhile favorites upon his official introduction into ALCS. When Trot Nixon stepped to the plate a little bit after 1 a.m. ET on Sunday, his mission was to sink his former team, not to mention the fans who cheered for him for so many years.
Serving as a pinch-hitter, Nixon did just that, blooping an RBI single to center with one out in the top of the 11th inning against lefty specialist Javier Lopez to snap a 6-6 tie.
"It was a situation where obviously Lopez is not a very comfortable at-bat for left-handers, dropping down submarine," said Nixon. "I was excited to finally get in there at 1:30 in the morning."
The Indians piled on from there, with Franklin Gutierrez's three-run homer off Jon Lester capping the massive damage.
The Indians started their winning rally when Grady Sizemore singled against Eric Gagne with one out. Asdrubal Cabrera followed with a walk. Then Nixon came on to pinch-hit for Josh Barfield, who had entered the game earlier as a pinch-runner for Travis Hafner. Nixon got just enough of Lopez's 79-mph offering to drop it in front of Boston center fielder Coco Crisp.
"It's just unfortunate that it kind of ended the way it did," said Lopez. "It was a cutter away off the end of the bat, [and it] found the hole. The guy knows Fenway better than anybody. It was just one of those pitches. I tried to execute my pitch and it was just a good piece of hitting."
The Red Sox liked their chances of emerging with a walk-off win in the bottom of the ninth. Dustin Pedroia belted a two-out single against Rafael Betancourt. Speedy Jacoby Ellsbury came on as a pinch-runner. Before you could say "Dave Roberts," Ellsbury stole second, setting up Kevin Youkilis with a chance to end the game with one swing.
Youkilis worked an 11-pitch at-bat and then lined one to center, but Sizemore got there just in time to catch it.
"We battled and played hard and played tough," said Youkilis. "It just didn't go our way at the end."
The Red Sox were even-keeled after the tough loss.
"It's not difficult to rebound from, not given the makeup of this team," said right-hander Curt Schilling, who took a no-decision. "There's no one that should feel bad in the clubhouse but me. Everything about this one falls on me."
At the beginning, the game was supposed to be a fierce pitchers' duel between Schilling and Cleveland co-ace Fausto Carmona. But Schilling -- who came in 9-2 in 16 postseason starts -- lasted just 4 2/3 innings, giving up nine hits and five runs. Carmona went four-plus innings before being removed after 95 pitches. He surrendered four hits and four runs while waking five and striking out five.
Ever the competitor, Schilling was not pleased with his performance.
TOUCHING 'EM ALL
With his two-run homer in the fifth inning, Manny Ramirez now has the most long balls in postseason history.
The big blow against Schilling was a three-run homer by Jhonny Peralta in the fourth that turned Boston's 3-1 lead into a 4-3 deficit. Sizemore added a solo shot in the top of the fifth.
Down, 5-3, in the bottom of the fifth and facing lefty Rafael Perez, the Red Sox got an equalizing two-run blast by Manny Ramirez that landed in the Boston bullpen in right-center. For Ramirez, it was his 23rd career homer in postseason, putting him first on the all-time list ahead of Bernie Williams.
Then it was Mike Lowell's turn to deliver, and he did, sending a towering drive off the Sports Authority sign behind the Green Monster Seats. That gave the Red Sox a 6-5 lead. It was the fifth time in club history the Red Sox produced back-to-back homers in a postseason game.
It seemed like nothing deflated the Indians. They got the tying run right back in the sixth against Manny Delcarmen, thanks to a walk to Peralta, a single to right by Kenny Lofton and a fielder's choice RBI to short by Gutierrez.
The tie lasted for hours.
"I didn't think this was going to be an easy series," said Lowell. "We have a big Game 3 -- literally tomorrow now. [We need to take the] same approach -- go after them and go get 'em. Hopefully we can go up 2-1."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.