In 1996, Roberto's 12th-inning home run helped Baltimore eliminate Cleveland in four games. The next year, it was Sandy who caught the third strike to his brother for the final out as the Indians upset the Orioles.
Those moments were bittersweet as the brothers' emotions were fractured, one's by sympathy and the other's by elation.
"I won that first year and Sandy won the second," Roberto said. "We're both professionals. But it's hard to play against your brother. Now we don't have to worry about that."
That became guaranteed Tuesday as Roberto Alomar, one of this winter's most prized free agents, was officially welcomed by the Indians, who gave the nine-time All-Star second baseman a $32 million, four-year contract with the hope he can finally fill their most problematic position.
But for the Alomar family, Roberto's arrival in Cleveland represents much more.
"This has always been a dream for us, and to me, now this dream has finally come true. It's a special moment for us," said Roberto Alomar, joined at the Jacobs Field news conference by his fiancee, tennis star Mary Pierce, and his father, Sandy Sr.
"I think baseball is real important, but family is more important."
Following the news conference, which was also attended by Indians owner Dick Jacobs and Cleveland manager Mike Hargrove, Roberto Alomar fondly recalled the first time he and his older brother were teammates.
"When I was a little kid, Sandy took me by the hand to his practice," Roberto recalled. "The coach asked who I was and Sandy told him. Then the coach asked, 'Can he play?' and Sandy said I could. I made the team as a 7-year-old and played on a team with kids that were 9-to-12.
"That's how I started playing baseball. Sandy took me. Hopefully, I can end my career here in Cleveland, win a World Series and end that chapter, end that book."
That's exactly the ending the Indians, who haven't won a World Series since 1948 but have lost two Series in the last four seasons, are hoping for too.
Cleveland, which has won four straight AL Central titles, had used 15 players at second base since trading away Carlos Baerga in 1996.
"One of the pieces that has been missing for our ballclub has been a second baseman," Indians general manager John Hart said. "In the case of Roberto, we are bringing in a potentially future Hall of Famer."
Roberto Alomar, coming off an $18 million, three-year contract with Baltimore, gets a $1 million signing bonus, $6.5 million next season, $7 million in 2000, $7.5 million in 2001 and $8 million in 2002. Cleveland has an $8 million option for 2003 with a $2 million buyout.
Sandy gets $2.65 million this season and the Indians have a $2.7 million option for next year.
The Alomars are the seventh set of brothers to play for the Indians, and the first since Gaylord and Jim Perry (1974-75).
"We're getting Robbie in his prime," Hart said. "And we want this obviously to be Robbie's last stop."
Whether Hart has stopped making moves this winter remains to be seen. Alomar's signing may have pushed Cleveland's payroll too high to pursue free agent starters Randy Johnson or Kevin Brown, but Hart said he is still willing to make a trade.
Hart already has bolstered the club's bullpen, acquiring relievers Jerry Spradlin and Ricardo Rincon in separate trades earlier this month.
Rincon, who was in town for a physical, also attended the Alomar news conference. After presenting the left-handed reliever with his jersey, Hart joked: "You don't have a brother who's a No. 1 starter, do you?"
Roberto Alomar, a career .302 hitter and seven-time Gold Glove, gives the Indians a current or former All-Star at every starting position and a middle defense second to none in baseball.
Alomar, 30, will now play alongside smooth and steady shortstop Omar Vizquel, a six-time Gold Glove who last year alone was paired with seven different second baseman.
The two could make pregame infield practice a must-see event for Indians fans.
"I've played with some great shortstops," said Roberto, who named Garry Templeton, Tony Fernandez, Alfredo Griffin and former Orioles teammate Cal Ripken. "But to be with Omar, sometimes he makes plays that are just incredible. It will be more fun to watch him beside him than to be in the opposite dugout."