But as the Yankees shortstop has done many times against the Red Sox -- not to mention a lot of other teams -- he came up with the big hit. Jeter launched an 84-mph offering from Schilling well over the Green Monster for a two-out, two-strike, three-run homer that silenced Fenway Park, broke a tie and ultimately delivered a 4-3 win for the Yankees.
"We were on the same page, we called the right pitch," said Schilling. "I just hung a split."
As it turns out, Jeter did deliver the parting shot of the night. But David Ortiz, Boston's version of Mr. Clutch, had a chance to one-up the New York captain and give Fenway Park one of his signature walk-off hits.
Mike Lowell had homered in the eighth off Joba Chamberlain to bring Boston within two runs.
And in the ninth, what drama unfolded against Mariano Rivera, the great closer of the Yankees. Jason Varitek led off with a walk. With two outs, Julio Lugo ripped a double to the gap in left-center and the Red Sox were down just one. Jacoby Ellsbury was hit by a pitch. In one of the better at-bats of the season, Dustin Pedroia, after falling behind 0-2, worked an eight-pitch walk to load them up for Big Papi.
"When I got two strikes, I was just trying to move it to the next guy," said Pedroia. "I wasn't trying to do too much. I wasn't trying to hit a home run, I wasn't trying to do anything. Just trying to get David to the plate because when you're facing a guy like that, he's the best closer of all-time. It's definitely not fun facing him but I had to fight my way on."
Ortiz was next to put up the big fight, hoping to end a game with one swing for the second time in five days. He worked the count to 2-2, then got one of those nasty high, inside cutters from Rivera and popped it up into shallow left-center. Jeter -- who else? -- ranged back, clutched the ball and pumped his fist.
"Went out there and fought like I normally do and he won the battle," said Ortiz.
Just like that, the 18-game series between the two American League East heavyweights ended, with the Yankees winning the season series, 10-8. However, the Red Sox still lead the American League East by 4 1/2 games with 12 games left. The Yankees have 13 contests remaining and lead the Tigers by 2 1/2 games in the Wild Card standings.
It was fitting for the final regular season act to come down to such a frenzied situation when you consider the way the teams have fought each other all year.
"We gave ourselves a chance," said Red Sox manager Terry Francona. "That doesn't make us feel a lot better tonight because we lost, but we did some good things to try to win. We'll take that spot again with David hitting."
It's not inconceivable these two teams could meet up again in the AL Championship Series.
Does Ortiz think it will happen?
"Probably, probably," said Ortiz. "They're playing well. You can never describe what's going to happen later on, but at least we don't have to deal with them for a while."
Before the tense ending, the game was all about Schilling and Clemens -- two of the greats of this generation, who were facing off for the first time since Game 7 of the 2001 World Series.
Schilling went 7 2/3 innings and gave up six hits and four runs while striking out two.
"I don't question whether I can be a really good pitcher and be successful and win," said Schilling. "Tonight boiled down to two mistakes. I missed horribly in probably the most crucial situation in the game."
Clemens, making his first Fenway Park start since Game 3 of the 2003 ALCS, fired six innings and allowed two hits and one unearned run while striking out four.
"A lot like Schill, he certainly hasn't forgotten how to pitch or compete," said Francona. "I thought early on, it looked like he was trying to get in the flow of the game."
The night started in ominous fashion for Clemens when Sox leadoff man Ellsbury clanged a line drive right off the glove of Johnny Damon in left field.
The error put the Red Sox in position to score their first run. With one out, Ortiz drew a walk, and Lowell -- who was in the middle of just about everything the Sox mustered offensively all night -- followed by slamming an RBI single to left to make it 1-0.
From there, the two veteran pitchers dominated for the next several innings. Clemens took a one-hitter into the bottom of the sixth. Schilling, aside from giving up a Robinson Cano solo homer in the fifth that tied it, was pinpoint. He threw 69 pitches over the first seven innings.
The Red Sox finally produced a rally against the Rocket in the sixth, when Ortiz drew a one-out walk and Lowell laced a single to right. With two outs, Jason Varitek lined one into left, only to see Damon rob him on a terrific diving catch.
That was the last pitch for Clemens. Coming off an elbow injury that forced him to miss one start, Clemens came out after 87 pitches.
Schilling has long admired Clemens, and that didn't change after this one.
"He does what he does when he doesn't have his best," said Schilling. "He grinds it out and makes pitches in big spots."
With the Red Sox and Yankees, it always seems to come down to big spots. On this night, it was Jeter who came through with the hit that counted most.
"I don't like seeing him come up in situations like that because he so often fights the ball to right field when you make a pitch," said Francona. "And if you leave a split up, he can do that also. You'd rather not see him in those situations."
The Yankees would say the same about Ortiz. But this time they survived.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.