Matsuzaka took a no-hit bid into the seventh inning and worked out of trouble all game, pitching the defending World Series champions past the Rays 2-0 Friday night in the ALCS opener.
Dice-K wiggled out of trouble in the first and seventh, then got help from his bullpen to rebuff one more threat in the eighth as the Red Sox taught the young Rays about dominant postseason pitching.
"It's amazing. We always joke how he gets out of these innings," Boston's Kevin Youkilis said. "He'll have bases-loaded, nobody out; or first and third, nobody out, and he gets out of jams. We wish he wouldn't put himself in those jams, but it's amazing how he does it and shows how great of a pitcher he is."
Jed Lowrie snapped a scoreless tie in the fifth with a sacrifice fly against James Shields, and Youkilis drove home another run with a seventh-inning double off left fielder Carl Crawford's glove as the playoff-savvy Red Sox beat baseball's best home team on its own turf.
Jonathan Papelbon closed out Boston's team-record sixth straight postseason road win. Now the upstart Rays, who held off the Red Sox for the AL East title, are the ones doing the chasing.
Game 2 is Saturday night at Tropicana Field, with Josh Beckett pitching for Boston against All-Star Scott Kazmir.
"This is probably how it's going to be," Youkilis said. "It's going to be a battle every game."
Crawford singled leading off the seventh for Tampa Bay's first hit and raced to third when Cliff Floyd followed with a single. But Dice-K, who was unbeaten on the road this season, was equal to the task.
Dioner Navarro flied to shallow left, Matsuzaka fanned Gabe Gross for the last of his nine strikeouts and Jason Bartlett grounded into a force play to end the threat.
"You have to tip your cap to Dice-K and the way he got out of jams," Shields said. "He was the better man tonight."
The Rays, who thrived on timely hitting in winning a franchise-record 97 games this season, missed another opportunity in the eighth after Matsuzaka, who allowed four hits in seven-plus innings, gave up two more singles.
Hideki Okajima relieved and Carlos Pena flied out on a 3-0 pitch. Justin Masterson took over and got All-Star rookie Evan Longoria to ground into a double play.
"Listen, it happens," Rays manager Joe Maddon said. "When you're facing very good pitching at this time of the year, they can stifle you even with nobody out. We can do the same thing to them."
Papelbon pitched the ninth for Boston, extending his career postseason scoreless streak to a major league-record 20 2-3 innings over 13 appearances. Joe Niekro held the old mark of 20 scoreless innings.
The Rays finished 1-for-7 with runners in scoring position. They wasted a big chance in the first, too, after Matsuzaka walked the bases loaded.
"He doesn't give in," Boston manager Terry Francona said. "He throws all his pitches, so hitters have to respect, even in tight situations, he doesn't become a one-pitch pitcher."
Much was made before the best-of-seven series about previous scuffles between the teams, a history both sides tried to play down. But the opener did turn a bit testy in the eighth when Grant Balfour hit J.D. Drew in the right shoulder with a high fastball, prompting a few Red Sox to holler from the bench.
Jason Bay drew a leadoff walk in the fifth and went to third when Mark Kotsay doubled down the left-field line for the third hit off Shields, who also started Game 1 for Tampa Bay in its first-round playoff series against the Chicago White Sox.
Lowrie, who drove in the winning run with a ninth-inning single in Boston's division series-clinching victory over the Los Angeles Angels, followed with a sacrifice fly.
Shields avoided further damage when Jason Varitek grounded to second and Jacoby Ellsbury popped to shortstop Bartlett, who made an over-the-head catch in shallow center field.
"I'm not discouraged in any way," Maddon said. "We played well, and we just have to hit better tomorrow, that's it."
The Rays breezed into the ALCS by beating the White Sox in their first-ever playoff series, while the Red Sox are playing for the pennant for the fourth time in six years after beating the Angels in the other ALDS.
With fans clanging cowbells and standing and cheering every strike, Shields fanned Ellsbury to start the game, then quickly slipped into a tight spot when Dustin Pedroia walked on a 3-2 pitch and Youkilis hit a drive to right that landed just inside the line and bounced over a short fence in foul territory for a ground-rule double.
Pedroia, who would have scored easily if the ball had not gone into the stands, rounded third and headed home where plate umpire Tim McClelland waited a few feet up the line. Shields escaped by striking out Drew.
Matsuzaka, 18-3 overall, also got off to a shaky start, walking leadoff man Akinori Iwamura and two of the next four batters to load the bases with two outs.
Opponents were hitless in 14 at-bats against the right-hander with the bases loaded during the regular season, and he got out of another jam by retiring Floyd.
"He just missed on a few pitches," Varitek said of the rocky first. "He did settle into his rhythm and found his arm slot more."
Tampa Bay won the season series between the AL East rivals 10-8, including eight of nine at Tropicana Field.
The Red Sox were 7-2 against the Rays at Fenway Park. Both of Tampa Bay's victories there came during a 10-day, confidence-building stretch in which the Rays took four of six from the World Series champions to hang onto first place.
Floyd, one of veterans brought in last winter to provide leadership in Tampa Bay's clubhouse, expects the talented Rays to rebound.
"We've come back from much worse situations than this," he said. "That's a good team. You've got to make sure that you capitalize when you have chances. When you don't, you're going to settle into an unfortunate situation like this."
Notes:@ Boston hasn't lost on the road in the postseason since losing at Cleveland in Game 4 of the 2007 ALCS. ... Since becoming the second player in major league history to homer in his first two playoff at-bats, Longoria is 2-for-14 with eight strikeouts. One of those hits also came in Tampa Bay's Game 1 victory over Chicago in the ALDS. ... Youkilis was 0-for-17 lifetime against Shields before his first-inning double.
