And both times, the New York Yankees came out on top.
Jeter hit a three-run homer off Schilling to break an eighth-inning tie and Rivera got Ortiz to pop up with the bases loaded for the final out Sunday night as the Yankees held off the Red Sox 4-3 and cut Boston's AL East lead to 4½ games.
"It's an honor to watch the best clutch hitter in history do his thing, and the best closer in history do his thing," said Roger Clemens, who in his first start since Sept. 3 dueled Schilling to a 1-all tie before leaving after six innings. "Jeter is one of the reasons that I got up off the couch and came back."
Schilling (8-8) outlasted Clemens but couldn't beat Jeter, who drove a 2-2 splitter over the Green Monster to give the Yankees a 4-1 lead. Joba Chamberlain and Rivera held on, even after Boston cut the deficit to one and loaded the bases in the ninth.
The Red Sox have a magic number of nine to clinch their first division title since 1995, but the Yankees won the season series 10-8 -- the first tiebreaker should the teams finish the year with the same record and both qualify for the playoffs. New York won six of the final seven meetings after Boston took the first four.
The Yankees, who lead Detroit in the AL wild-card standings by 2½ games, have won nine of 11 overall.
"We still have our fate in our hands," Yankees manager Joe Torre said. "We can't look for help."
Jeter is batting .441 with runners in scoring position and two outs - the best mark in the majors.
"Even when you're a little kid you think about those situations," he said. "Every time you envision yourself in those situations, you come through. ... I like those situations."
Chamberlain (2-0) allowed one run and two hits, striking out three to earn the victory despite giving up the first earned run of his career -- and Mike Lowell's third hit of the night -- a solo homer that made it 4-2.
Rivera gave up Julio Lugo's two-out RBI double in the ninth, then hit Jacoby Ellsbury with a pitch and walked Dustin Pedroia. Ortiz popped up a 2-2 pitch into shallow center field, and a backpedaling Jeter made the catch before pumping his fist.
It was Rivera's 28th save of the season.
"It kind of seems appropriate that when we play them it should come down to something like that," Red Sox manager Terry Francona said. "We gave ourselves a chance. We came up short, but we'll take that spot again with David batting."
Schilling allowed four runs and six hits, striking out two in 7 2/3 innings. He fell to 0-3 in his last four starts.
The right-hander gave up Robinson Cano's leadoff homer in the fifth, then retired 10 straight batters before Doug Mientkiewicz singled with one out in the eighth. Jason Giambi, out of the starting lineup so banged-up catcher Jorge Posada could DH, pinch hit and lined a single high off the Green Monster.
Johnny Damon dribbled one off a broken bat, requiring a nice play by second baseman Pedroia to hold the runners and get the out at first. Jeter fell behind 1-2 before giving the Yankees the lead and chasing Schilling from the game.
"I missed horribly in probably the most crucial situation in the game. I can't do that," Schilling said. "This is an incredibly painful way to learn a lesson that you already know. So many things I could have done there, and I did it as wrong as I could do it."
Matching up for the first time since Game 7 of the 2001 World Series, Schilling and Clemens dueled to a 1-all tie through 6½ innings before Chamberlain relieved Clemens to start the seventh. Chamberlain had not allowed a run in 17 2/3 innings over 13 appearances before Lowell connected.
The 45-year-old Clemens, coming back from a blister on his foot and ligament damage to his right elbow, allowed one unearned run, two hits and three walks. He struck out four -- all in a row in the third and fourth.
- A fan chased Boston's Eric Hinske to second base when he doubled in the seventh, tried to high-five him and then stole Cano's hat before fleeing into left field. He was apprehended, roughly, by security.
- Posada was in the lineup at DH instead of catcher, one day after being knocked over in a home plate collision with Hinske.
- Ellsbury failed to hit safely for the first time in 14 games since being called up from the minors on Sept. 1.