So on Tuesday night, the visitors left nothing to chance in a roller-coaster of an 8-4 win.
Not Francona, who called on closer Jonathan Papelbon with the bases loaded and nobody out in the eighth.
Not Papelbon, who fired an array of nasty pitches and refused to buckle en route to the first six-out save of his career.
And certainly not center fielder Jacoby Ellsbury, who made the play of the game and one of the stand-out moments of the season, robbing Jason Bartlett with a do-or-die diving catch that could have ended in sheer disaster.
"We did a lot of good things tonight and we had to," said Francona. "We've had a lot of miserable nights here. We did a lot of things for it not to be a miserable night."
Winning under the roof of Tropicana Field, where the Red Sox had lost 14 out of 16 dating back to Sept. 23, 2007, was no small feat.
And it couldn't have come at a better time.
With the Red Sox in a fight make it to the postseason for the sixth time in the past seven years, they were able to distance themselves further from the Rays, the team that knocked them out in Game 7 of last year's American League Championship Series.
Tampa Bay is in third place in the Wild Card standings, trailing the Red Sox by six games. The Rangers, meanwhile, swept a doubleheader from the Blue Jays to pull within 3 1/2 of Boston.
"The biggest thing I liked about it was we got a win here -- we got a win on the road in Tampa Bay," said Ellsbury. "For some reason, it's been tough for us, but it was a nice win tonight. It just puts them back another game. Any time you play them head-to-head, those are big games with a month left in the season. It's nice to come in here and get that first one."
Not only was it nice, it even seemed easy for a few innings.
Jon Lester -- who earned win No. 11 -- put on his latest power-pitching clinic, striking out nine over six innings. With 196 strikeouts, Lester surpassed Bruce Hurst (190 in 1987) for most by a southpaw in club history.
Billy Wagner turned in a dominant seventh inning (two strikeouts) in his second outing for Boston. The offense applied steady pressure, backed by home runs from J.D. Drew (seventh in the past 19 games), Jason Bay (No. 30) and Kevin Youkilis.
There the Red Sox were, up 7-2 going into the bottom of the eighth. With the normally dependable Hideki Okajima opening the inning, it seemed as if Papelbon wouldn't be called on until the ninth, if at all.
But Evan Longoria, who usually torments the Red Sox with home runs, led off with a bunt single. Carlos Pena drew a walk. Pat Burrell lined a single to left, driving in Longoria. Then, frustrating things started to happen. Pinch-hitter Willy Aybar blooped a single just out of the reach of second baseman Dustin Pedroia and into short right field, loading the bases. Dioner Navarro then blooped a hit in virtually the same spot, bringing in another run and making it 7-4 with the bases still at maximum capacity and nobody out.
"You know it's a big game when you bring your closer in with no outs in the eighth," said Ellsbury.
On came Papelbon, and down went B.J. Upton, who struck out on 94-mph heat. Bartlett stepped up next and lined a 2-2 pitch to center. The safe play would have been for Ellsbury to field it on a hop and concede a run. But he was more interested in trying to win the game, so he sprawled out for it and made his second highlight-reel play of the game.
"I caught it right in the heel," said Ellsbury. "That's one of those plays where you have to catch it. If it gets by me, it's probably an inside-the-park home run or maybe at best, a triple. It's one of those plays you have to make."
And he made it, leaving Papelbon with one last task, retiring the dangerous Carl Crawford. It took nine pitches, but Crawford flew to left, and the Red Sox had made one of their most dramatic escapes of the season.
"I was doing anything to keep the at-bat alive," Crawford said. "He got the best of me there. We were hitting Okajima pretty good, or they were finding base hits and I guess [Francona] didn't want to take a chance and brought [Papelbon] in early."
The key, Papelbon thought, was that he didn't get too amped up.
"I try not to get any more fired up," said Papelbon. "I try to keep telling myself the coolest guy is going to win those situations because those are pressure situations. When you get in pressure situations, the guy that's the coolest is always going to come out on top."
With the bases loaded this season, opponents are 1-for-15 with 10 strikeouts against Papelbon.
"You get the best of him in those situations," said Francona.
Nobody could relate better to what Papelbon accomplished than Wagner, who has 385 career saves.
"I told him I'm glad it's him and not me. That two-inning thing, that's for young people, not for me," said Wagner. "It was very impressive. I told him that was great. That was a lot of fun to watch. I know the nerves and what's going on out there. One bad pitch and you look like the goat. But man, he was great tonight. That was fun to watch."
It was Papelbon's 33rd save in 36 opportunities. But the save within the save went to Ellsbury.
"Oh boy," said Francona. "When he came in, I told him, 'Jake, if you missed that and it rolls, just go right up that tunnel and go right out with it.' I was obviously teasing him, but that's a game saver. They had runners moving. It was a heck of play."
And considering the venue and the calendar, also a heck of a win.
"Huge," said Papelbon. "Especially the first game of the series. It's definitely big to get the first game of the series and set the tone."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.