Daisuke Matsuzaka’s fastball hummed and his curveball darted. His offspeed pitches were mostly unhittable, too.

The Boston right-hander had it all going Friday night, shutting down the Tampa Bay Rays during a 2-0 victory that put the Red Sox on top in the best-of-seven AL championship series.

‘‘He looked unbelievable,’’ said Kevin Youkilis, who was 3-for-4 with a RBI double for the defending World Series champions, who have won the opening game in five consecutive postseason series.

Especially while working out of trouble to remain unbeaten on the road this year.

‘‘He doesn’t give in,’’ Red Sox 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.’’

Matsuzaka took a no-hit bid into the seventh inning and Boston’s bullpen bailed him out of a jam in the eighth as the playoff-savvy Red Sox beat baseball’s best home team on its own turf.

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.

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 doing the chasing.

Game 2 is at Tropicana Field on Saturday night, with Josh Beckett pitching for Boston against All-Star Scott Kazmir.

The young Rays, who won 97 games after finishing with the worst record in the majors a year ago, expect to rebound.

‘‘We know what we’re capable of doing,’’ Rays designated hitter Cliff Floyd said.

‘‘We’re going to dwell on it for 30 minutes and shut it down and get ready to go,’’ Shields said. ‘‘That’s what we’ve been doing all year, and I don’t think we’re going to change much.’’

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.

‘‘The way our infield was set up, we were prepared to give up the run for a couple of outs,’’ Matsuzaka said through a translator. ‘‘After I was able to get the first batter out, it certainly got a lot easier.’’

The Rays, who thrived on timely hitting all 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.