Cleveland suffered a setback in their bid to reach the World Series after crashing to a 7-1 defeat to Boston in the American League Championship.
Beckett gave a dazzling pitching performance for Boston
Josh Beckett had 11 strikeouts as the Red Sox pulled back to 3-2 down in the best of seven play-offs series.
Beckett allowed just one run on five hits to send the teams back to Fenway Park for game six on Saturday.
The Indians need to win at least once in Boston to book a World Series showdown with the Colorado Rockies.
National League champions Colorado have already booked their passage into the World Series after sweeping Arizona in the National League decider.
Cleveland, meanwhile, had recorded three straight victories going into the match after losing the opener.
But despite the loss, Cleveland boss Eric Wedge remained optimistic of his team's chances.
"You talk about beating a team like Boston four in a row, that's tough to do, particularly in the post-season," Wedge said.
"But we put ourselves in a pretty good position the way we played here at home."
Only 10 times in post-season history have teams fought back from 3-1 deficits to win a best-of-seven series.
The last were the 2004 Red Sox, who rallied from 0-3 down to beat the New York Yankees on their way to winning the World Series title.