Had the Indians faltered in either of those two segments, they might not have basked in the glow of an 8-4 victory in which they avoided a three-game sweep at the hands of the Red Sox and finished up a nine-game, three-city road trip with a 5-4 record.
"The guys really played their tails off this whole trip," manager Eric Wedge said. "Those were three hard-fought games here. I thought we played good baseball here."
But while the baseball might have been good, the Tribe's results the first two nights were far from satisfactory.
So when Paul Byrd got the ball in opposition of Dice-K, Byrd knew it was an important start.
"I think it means a little extra when you're trying to stop a slide," Byrd said. "And I think it means something extra when you're in first place and you have a team a game or two behind you. It's a little extra pressure."
The Indians' lead in the American League Central is now 2 1/2 games over the Tigers -- their opponent this weekend at Jacobs Field -- in large part because of Byrd's efforts in the face of that pressure.
Byrd won his fourth start in a row with another aggressive attack of the strike zone. He threw a first-pitch strike to 25 of the 27 batters he faced in six-plus innings, and, as has become the standard, he didn't walk anybody, running his streak without allowing a free pass to 43 innings.
"He controlled the ballgame again," Wedge said of Byrd. "He made pitches when he had to and stayed away from the big inning."
The Indians put together two big innings in support of Byrd -- one on the offensive end against Matsuzaka and the other when Byrd left behind a bases-loaded jam in the seventh.
Dice-K was putting together an effective, if not efficient, outing against the Tribe through four innings of work.
But the Indians erased a 2-0 deficit in the fifth to set up a sixth inning in which their bats, which had been downright stagnant the first two games of this series, really came alive.
Trot Nixon opened the sixth with a double, and David Dellucci followed that one out later with a double of his own to drive Nixon in and give the Indians their first lead of the series, 3-2.
"David had a big hit for us," Wedge said. "He's a guy I'm rooting for, and he's starting to come around."
Dellucci came around to score on a Josh Barfield single that would have been a double, had Barfield not overrun second and got caught off the bag by Manny Ramirez's throw from left and Dustin Pedroia's phantom tag.
No matter, though. With two outs, the Indians continued to unload with Kelly Shoppach's single and Grady Sizemore's two-run homer to right.
Just like that, it was a 6-2 ballgame and Matsuzaka was gone. The Indians had been interested in seeing what a $103.11 million investment could buy, and they seemed to have no trouble adjusting to Dice-K's stuff.
"We've all faced great pitchers many times," said Shoppach, who had a four-hit night. "With our offense, there's no giving in. We deserve a little bit of credit of putting our nose in there and getting after some tough pitches against a tough pitcher and chasing him out of there earlier than the last two guys [Curt Schilling and Josh Beckett]."
The way Byrd was pitching, he didn't look as though he'd be chased early. He threw just 71 pitches through six innings, and he had what seemed to be a comfortable cushion.
But in the bottom of the seventh, the Red Sox got to Byrd in the form of three straight singles with none out. Wedge yanked his starter and put in Tom Mastny, who wasted no time getting Coco Crisp to pop out into foul territory and striking out Kevin Youkilis.
The biggest threat, though, was still looming in the form of Ortiz. While game-tying grand slams might not be an everyday occurrence, they seem to be a distinct possibility whenever Big Papi steps to the plate in such situations.
This situation was placed in the hands of Fultz, who had struggled with his command throughout this road trip.
"The one thing you have to do is slow the game down," Fultz said. "You take a deep breath and go after him."
In a nine-pitch at-bat, that's just what Fultz did. And Ortiz nearly took him deep when he hammered a fastball down the right-field line. Fortunately for Fultz, it sliced foul.
Fultz's next offering was a 2-2 curveball, and Ortiz lined it weakly to Casey Blake at third with the final out.
"It wasn't a very good swing," Fultz said. "Anytime you can get a guy like that out and it's not a very good swing, that's good."
The Indians, who pounded out a season-high 18 hits on this night, had to label this a good road trip, given that they're in a stretch of 20 games in 20 days and they swept the division-rival Tigers along the way.
"We knew this was going to be a challenging stretch for us," Wedge said. "Our guys were up for it."