While Boone appeared to wait too long to get Luis Severino out of the game when the right-hander's command was lacking, Cora opted to insert Brock Holt into the lineup at second base and start Nathan Eovaldi.
Since those decisions worked out for Cora, the Red Sox can secure their trip to the American League Championship Series by beating the Yankees Tuesday in Game 4 of the American League Division Series.
Rick Porcello will start for the Red Sox against New York left-hander CC Sabathia.
The Red Sox need one win to reach the ALCS for the first time since 2013 when they won their most recent championship. If they are unable to get it Tuesday, Game 5 is Thursday at Fenway Park.
The Red Sox and Yankees are in their respective positions because of what unfolded Monday when Boston cruised to a 16-1 rout.
Holt went 4-for-6 to become the first player to hit for the cycle in a postseason game, capping the milestone with a two-run homer in the ninth off New York backup catcher Austin Romine. Eovaldi, who was originally going to start Game 4, gave the Red Sox seven strong innings and helped hold the Yankees to five hits.
"We're going to try to take this into tomorrow," Boston left fielder Andrew Benintendi said. "It's over. We've enjoyed it. Now we can focus on tomorrow and get after it."
Holt had two hits in the decisive seven-run fourth that was highlighted by Benintendi's bases-clearing double.
Those hits occurred after Boone lifted Severino with the bases loaded and nobody out. Severino's fastball velocity was diminished slightly and he was tagged for six runs on seven hits in three-plus innings.
"I mean in hindsight because he didn't get an out," Boone said.
Now because of the decisions, the Red Sox will get a chance to clinch their second postseason series win in New York, nearly 14 years after coming back from 3-0 down in the ALCS.
"No choice but to flush," Boone said after New York absorbed its worst postseason loss. "The good thing about today is it's one game and, as awful as of a night it was for us, we got to turn the page, and tomorrow's obviously do or die."
The Yankees trail a series two games to one for the third straight time. They won Game 4 from Cleveland in the ALDS last season and Game 4 of the ALCS from Houston a year ago.
New York is hoping to force a fifth game in Boston and its history, the only times the Yankees did not force a fifth game after falling behind in the ALDS two games to one was 2002 vs. the Los Angeles Angels, 2006 against the Detroit Tigers and 2007 vs. the Cleveland Indians.
Porcello threw 15 pitches in getting two outs in the eighth inning Friday and protecting a two-run lead. He exited after allowing an infield single to Gleyber Torres, resulting in Craig Kimbrel getting the final four outs around Aaron Judge's solo homer.
"I think he'll obviously be ready," Holt said. "We're lucky to have him on the mound, that's for sure."
As for Porcello's postseason history, it is inconsistent so far. He is 0-3 with a 5.33 ERA in 12 appearances and is 0-1 with a 7.00 ERA in four postseason outings with the Red Sox.
Porcello made one postseason start against the Yankees in 2011 when he started Game 4 of the ALDS for the Detroit Tigers. Back then Judge was still at Fresno State and Sanchez completed his second season in the minor leagues in the South Atlantic League.
The Red Sox are hoping to see the version of Porcello, who was 2-0 with a 2.31 ERA in four starts against the Yankees during the regular season.
"He's actually been good against them," Cora said. "At one point of the playoffs, he was going to start regardless if it was Game 3 or 4."
CC Sabathia makes his 23rd postseason start and 24th appearance. In those appearances, he is 10-6 with a 4.20 ERA.
Sabathia has pitched particularly well in the ALDS. In 11 appearances (10 starts) he is 6-0 with a 3.32 ERA.
Since joining the Yankees in 2009 as a free agent, Sabathia is 8-3 with a 3.26 ERA in 18 postseason appearances (17 starts).
The veteran left-hander faced the Red Sox twice in the 2007 ALCS with Cleveland and was 0-2 with an 11.61 ERA while losing Games 1 and 5 of that series.
During the regular season, Sabathia was 1-0 with a 4.50 ERA in three starts against the Red Sox.
"Top to bottom, it's a tough lineup," Sabathia said. "They've got speed. They've got power. They take a lot of pitches. It's a good lineup -- bad lineup for me in the fact they take a lot of pitches, they're patient, and they do a good job of working the count."