But as they embark on what well could be their final visit to the legendary venue in the Bronx called Yankee Stadium, they are also aware that if they focus too much on nostalgia, they just must be history themselves, at least as far as 2008 is concerned.
Red Sox manager Terry Francona had time to reflect on Yankee Stadium while managing the American League All-Star team in July. This is a business trip.
"I guess I felt it more during the All-Star Game because it's the All-Star Game and you have time to think about things," Francona said. "But when we're playing a team it's always just trying to beat them. That's what I really care about. I don't get caught up with the other stuff."
Sure, the postseason doesn't start for another five weeks. That said, the Red Sox are basically in playoff-mode now, as each of their final 32 games figure to be crucial. This three-game series in New York will be a prelude to the last three games of the 2008 season for both teams, when the Yankees come to Fenway.
In a sense, this series could help determine if that final series will mean anything. Should the Red Sox sweep in New York, they would lead the Yankees by eight games in the Wild Card standings. If the Yankees sweep Boston, they would be right back in it, trailing by just two games.
"We're just going there to win a series," said Red Sox first baseman Kevin Youkilis. "If we win two out of three, it's only a one game jump [in the standings]. That's the way we look at it. We're not trying to bury somebody or anything like that. We're just trying to win every series from here on out. If we can win every series from here on out, we'd put ourselves in a good position to get to the playoffs. It doesn't matter if it's the Yankees or the Rays or White Sox or whoever. We're just trying to win a series and that's our whole goal."
For the two traditional American League East heavyweights, 2008 has been a struggle. Both teams have been hit with a truckload of injuries and they've had to rely on grit more than ever.
The defending World Series champion Red Sox trail the Tampa Bay Rays by 4 1/2 games in the American League East, and lead the Twins by one game in the Wild Card standings.
The Yankees trail the Rays by 9 1/2 games in the AL East, and the Red Sox by five in the fight for the Wild Card.
If the unthinkable happened and both teams missed the playoffs, it would be the first time since 1993, which is also the last time Yankee Stadium had the lights off for October, excluding the 1994 strike-shortened season. The Red Sox are vying for a fifth trip to October in the six seasons Theo Epstein has been general manager.
What that means is that there will be plenty of urgency for both teams in this latest showdown, which begins Tuesday night when the Red Sox activate knuckleballer Tim Wakefield from the disabled list for a start against Andy Pettitte.
Of all the players on the Red Sox, perhaps Wakefield will have the most appreciation for what could be his final start at Yankee Stadium.
"I've played against them in that stadium for the last 14 years," said Wakefield. "It's a very special cathedral in baseball and hopefully I'm around next year to see the new one."
Among players on the Red Sox, only Mike Timlin has visited Yankee Stadium more than Wakefield.
"I've had the chance to play there many, many years and I'm very happy that I've had the chance to play there," said Timlin, Boston's venerable righty reliever. "Knowing it's probably going to be our last trip in to that stadium, it's pretty special. You take it as it comes and it's a blessing to be able to play in that stadium. It's going to be pretty cool. I've had a lot of favorite moments there. I can't name one. I've had some special times there. It's hard to narrow it down."
The one defining moment the Red Sox will take with them from Yankee Stadium is Game 7 of the 2004 American League Championship Series, when Johnny Damon belted two homers, including a grand slam, to pace a 10-3 victory and lead Boston's historic comeback from a 3-0 series deficit.
Of course, Damon now plays for the Yankees, which is just another reminder of how much things change in modern-day baseball.
Perhaps the forever rivals have a few more memories to create in the next three days.
"Honestly, I haven't really thought about that. I think it probably won't hit you until you play in the new stadium next year," said Youkilis. "You don't really think about that stuff until it's gone. Things in life, you don't appreciate until it's gone. I think when we play next year in the new stadium, remembering all the memories of the old stadium, will probably be reflected."
Instead of focusing on the Yankees, the Red Sox will try to keep the tunnel-vision approach that has helped them win the World Series twice in the last four years.
"We're not worried about other teams," said Red Sox second baseman Dustin Pedroia. "We're worried about ourselves. We're just trying to come out and win every game we play. It doesn't matter if we're playing the Yankees or anybody. We're not looking forward or looking to anything. We're just trying to win every game we play."
And the next three will be against the Yankees, meaning some high-voltage electricity figures to be in the air.
Ian Browne is a reporter for MLB.com. David Singh, an associate for MLB.com, contributed to this report from Toronto. This story was not subject to the approval of Major League Baseball or its clubs.