BOSTON — By his own admission, Josh Beckett is a pitcher who lives in the moment, from pitch-to-pitch, inning-to-inning.

But if he’s not careful, Beckett might have to ignore the present and consider history.

His complete-game shutout in Game One of the American League Division Series last night marked his second straight postseason shutout — the last coming in Game Six of the 2003 World Series — and was his third in six career postseason starts.

That’s the kind of October performance that gets you mentioned with the game’s pitching greats.

Predictably, Beckett wanted no part of that context after toying with the Los Angeles Angels of Anaheim in a 4-0, four-hit whitewash in Game One.

“I think those are all things you should worry about when you retire,” said Beckett, “not really worry too much about them [now].”

But if last night is any indication, Beckett has the chance to establish himself as one of the game’s most clutch pitchers.

If he looks around his own clubhouse, Beckett can see another. Curt Schilling, the Red Sox’ Game Three starter, is 8-2 career in the postseason, with a World Series co-MVP of his own. (In his first season in Boston, Beckett had another teammate with the same credentials — David Wells, who is 10-5 in postseason baseball).

Beckett may be reticent to talk about his reputation, but others weren’t.

“I think he cares a lot about how he’s perceived in the game,” Terry Francona had said Tuesday afternoon, before the series got under way, “and what his goals are in the game. He’s got some pretty lofty goals.”

“He loves to compete,” said Kevin Youkilis, whose first-inning homer provided the only backing Beckett would need. “We’re fortunate enough to have Josh do that every [time he throws].”

The Angels, by contrast, were not fortunate at all, facing Beckett when the big right-hander had his full complement of pitches. After allowing a leadoff single to Chone Figgins, Beckett retired the next 19 hitters in a row.

“I don’t think you’re going to be able to pitch a much better game than that,” said Angels manager Mike Scioscia succinctly.

Finally, Vladimir Guerrero broke the streak with a single to center, but it led to nothing. Beckett simply began another run, setting down 8 of the final 10 hitters he faced. He didn’t walk a batter and struck out eight.

“He went out there and executed his pitches, in my opinion, probably better than he has at any point in the season,” said Francona. “He attacked the strike zone with all of his pitches. He pounded the strike zone with all three pitches.”

For a pitcher at the top of his game, the Angels were the perfect opponent. Never known for their patience, the Angels were as aggressive as ever, and when Beckett showed that he could throw first-pitch strikes and get ahead in the count, the Angels obliged by swinging early and giving Beckett some easy innings.

It took him just 108 pitches to blank the Angels.

Always highly self-critical, Beckett had been angry at himself that his last two September wins featured lengthy first innings. Those long innings drove his pitch count up and made it impossible for him to pitch deep into the game.

He took upon himself last night to correct that and be more efficient with his pitches.

“I just didn’t want to get wrapped up in trying to strike a lot of guys out,” he said, “because those are the at-bats that will end up killing your pitch count and you’re out after 5 1/3 because you’ve got 120 pitches.”

Beckett’s gem puts the Red Sox in command of this five-game series. And that’s where the other historical parallel comes in.

It used to be that great October pitchers were capable of carrying their teams through the demanding October obstacle course. Think Mickey Lolich in 1968, Orel Hershiser in 1988 and Jack Morris in 1991 as obvious examples.

The addition of the Division Series makes it more difficult, of course, for one man to do it by himself. Three rounds of play means a month-long postseason and 11 games to be won.

Along the way, Beckett will have help. Last night, he didn’t need any of it.

smcadam@projo.com