David Ortiz and John Olerud connected for back-to-back homers in the fourth for Boston, which matched their season high by moving 14 games over .500 at 59-45. For the third straight day, Olerud made his presence felt offensively, driving in eight runs during the three-game weekend sweep.
The win, combined with New York's come-from-behind 11-inning victory over the Angels, kept the Red Sox 2 1/2 games ahead of the second-place Yankees in the American League East.
Curt Schilling pitched the ninth to convert his fifth save in six tries as the Red Sox won their fifth straight contest.
Early on, the storyline belonged to a fire-balling 24-year-old right-hander making his Major League debut for the Red Sox.
Sporting a fastball that frequently touched 94 mph on the center-field scoreboard (topping out at 95 mph), Jon Papelbon blew away the Twins in the first three innings, yielding just one hit while striking out five.
Johnny Damon called Papelbon's stuff electric from his view in center. Catcher Jason Varitek didn't argue.
"I could kind of sense that in the bullpen a little bit," Varitek said. "He's got a great demeanor about him. He's got a good fastball and his offspeed stuff was a lot better than anticipated. He's got a good little heart on him. You can see that.
"You just want him to get his first out, period. Let him go from there. Don't complicate things and let him do what he can do. We sat, we talked, 'This is about you. This isn't about me. You go out there and teach me what you can do.' We talked before the game, we had a good game plan and he did an excellent job."
Papelbon struck out the first two batters he faced -- Shannon Stewart and Luis Rodriguez -- and finished with seven strikeouts in 5 1/3 innings.
"I wanted to start the game out just attacking hitters," Papelbon said. "Just go after them -- to let them know that I was out there to win a ballgame and put my team in a chance to win. I think once I got past that first inning, I settled down a bit.
"I was nervous, but I think I was just trying to get all the butterflies flowing in the right direction. Luckily, I was able to do that, and just go out there and let my ability take over."
Papelbon added his name to the growing list of pitchers impressed with the way Varitek calls a game.
"I can't give that guy enough respect," Papelbon said. "With him and me pitching out there, I felt 100 percent comfortable. I could just tell that every mannerism he made and every sign he threw down, that it was [with confidence].
Papelbon had plenty of support in the stands -- as many of his family members flew up from Jacksonville, Fla.
"I can't even explain it," he said. "This is something I've been looking forward to my whole life. My fiancée's family flew up from Mississippi. Just to have their support and to know they are behind me 100 percent really means the world to me."
Papelbon, however, struggled with his command beginning when he hit Jacque Jones in the second. Papelbon finished with five walks.
He left to a standing ovation from the 193rd consecutive sellout crowd at Fenway. Another young gun made his Fenway Park debut when Manny Delcarmen relieved Papelbon with runners at first and second and one out in the sixth.
Papelbon threw 100 pitches, allowing four hits and three runs (two earned) while surrendering solo homers to Justin Morneau in the fourth and Jones leading off the sixth.
Delcarmen struck out Nick Punto looking before getting Stewart to ground into an apparent inning-ending fielder's choice. But Bill Mueller's throw to second sailed wide of Alex Cora and into right-center, allowing Lew Ford to score from second.
One of the many ironies of the day came in the seventh, when the Red Sox tied the game, 3-3. Francona, who took responsibility for a lack of communication on Wednesday when Ramirez didn't play, took Ramirez aside in the dugout and went over the possibility of using him as a late-inning pinch-hitter.
"We always try to let every player know in advance where they could be, because obviously, one move leads to another," Francona said. "You try to have a game plan exactly [for] 'if this happens, you're going to do this.'"
Olerud, who had already homered and singled, felt a twinge in his hamstring running the bases in the seventh. He came out of the game in the top of the eighth, leaving Kevin Millar to move to first, Gabe Kapler to move over to left field and Adam Stern to come in and play right.
"Right in the middle of that inning, Olerud feels his hamstring," Francona said. "So that makes you do a little bit of a double-take, because that wasn't something we planned. So you have to take that into consideration."
When the Twins decided to intentionally walk David Ortiz with Edgar Renteria on second, Francona called on Ramirez.
"We obviously tried to pick a spot for Manny to hit," said the Sox skipper. "It's hard to do with an open base. You don't want to see him sit all day and wait for a spot and then walk him. It was a perfect spot."
And the perfect ending to what most inside the Sox clubhouse would agree was the most bizarre yet successful weekend of the season.