It has been a long time since the Red Sox and Yankees played a September series like this in which both teams had so much skin in the game. Maybe too long.

The Red Sox, who continue to be one of the great surprises in baseball this season, come into the three-gamer at Fenway Park as the leader in the American League Wild Card race, two games ahead of the Yankees. The Yankees? They just scratched their way past the Blue Jays to get into the second AL Wild Card spot by sweeping Texas. It is unlikely that both the Red Sox and Yankees will miss the postseason. But they both still could. And it is likely that one of them might.

So there will be the feeling and sharp edge of knockout September baseball for the first time in a while, when Gerrit Cole goes against Nathan Eovaldi. The Yankee ace against the guy who was the Red Sox’s ace until Chris Sale came back. By the end of this one, the Red Sox will be three up in the AL Wild Card with a week to play. Or the Yankees will be back to within a game.

The games between these two teams always seem to matter, of course. No one will ever forget when what is known as The Rivalry was as good and heated and memorable as it has ever been, and likely will be. There were 38 regular-season games played between the Red Sox and the Yankees in those seasons (2003 and ‘04; Boston won 20 and New York 18), and those were just the appetizers.

Because then they twice played each other in the most dramatic events between them since Bucky Dent’s home run won a one-game playoff between them in Fenway Park on Oct. 2, 1978, the year that the Yankees came from 14 1/2 games back to finally catch the Sox the last week of the regular season.

Then came 2003 and a Game 7 won by the Yankees in the bottom of the 11th of Game 7 of the ALCS at the old Yankee Stadium, where the current Yankees manager, Aaron Boone, hit a walk-off homer out to left off Tim Wakefield. The very next year, the Red Sox didn’t just come back. They wrote the greatest comeback in baseball history and maybe sport history, coming from three games to none behind, and finally winning Games 6 and Game 7 at the old Stadium, on their way to winning their first World Series since 1918, when they still had this guy Babe Ruth.

In memory, it seemed like all of the nine-inning games in those years tried to make it past four hours. There was an incident that ended with Pedro Martinez putting Yankees coach Don Zimmer on the ground. There was another one at Fenway, where Jason Varitek stuck his catcher’s mitt in Alex Rodriguez’s face to another fracas between the two teams. And that’s just the short list.

“I came to hate those games,” Joe Torre joked to me one time.

It was like that in 2003 and ’04. But nobody talks much about the race in the AL East between the two teams that happened in 2005, when they ended up tied at 95-67 after a three-game series at Fenway, and the Yankees won the division because they had won the season series from the Sox.

That season is worth remembering now because it also produced a September weekend series between them -- at the Stadium that time -- that feels like the one we’ll get this weekend at Fenway. That time, the Yankees were still trying to catch the Red Sox in mid-September, and the Indians had gotten hot enough to look as if they might knock out either the Sox or the Yanks from the AL Wild Card.

The Red Sox and Yankees had split the first two games of the series. The rubber game on Sunday was between Randy Johnson and Wakefield. It came the day after Johnson’s 42nd birthday, and even though his Yankees career was not what anyone expected it to be -- the following season he won 17 games with an ERA of 5.00 -- he produced not just his best performance as a Yankee, but one of the most intense 1-0 games any Red Sox-Yankees series had seen.

Johnson struck out eight that day against two walks in seven innings. The only run came on a Jason Giambi home run in the first. Wakefield only gave up three hits in defeat. The Yankees would go on to pass the Red Sox and take the division. The Red Sox got the one AL Wild Card spot in play in those days. In the end, Cleveland came up a couple of games short.

“That’s the pitcher that everybody expected, and that’s the pitcher that I expected,” Johnson said when it was over that day.

Cole against Eovaldi this time around. But a series, 16 years later, that feels a lot like the one in 2005. Three years ago, the Red Sox and Yankees played a hard, four-game division series that wasn’t settled until the bottom of the ninth of Game 4. This one, this weekend, feels a little like that. Sometimes this is The Rivalry in name only. Not this weekend at Fenway. A lot of skin in the game. For both of them. Like the old days.