BOSTON — Is it possible, even in some sort of wild Red Sox fantasy, that a team trotting out the likes of Jeff Bailey and Gil Velazquez can still win the American League’s Eastern Division title?

That dream is still alive this morning, if ever so slightly. After the Tampa Bay Rays lost in Detroit by a 7-5 count, the Red Sox rode a strong six innings from lefty Jon Lester to an easy 6-1 victory over the Cleveland Indians at Fenway Park last night.

With a magic number of one, the Rays lugged cases of champagne from Baltimore to Detroit’s Comerica Park in hopes of celebrating their first-ever division title. Those expensive bottles will remain chilled until the Rays beat the Tigers or the Sox lose once to the Yankees in this weekend’s three-game series that wraps up the regular season.

Of course, there is a razor-thin possibility neither scenario develops and the Red Sox somehow steal the division title away. The Sox players say they are not scoreboard-watching and, sure enough, when the Tigers finished off the Rays yesterday afternoon, only one Red Sox player [ Jacoby Ellsbury] was watching a TV in the team’s clubhouse.

“We’ve got to win out and they’ve got to lose out. We can’t control what they do,” said catcher Jason Varitek. “We’ve got to do a little bit of both (winning and getting ready for the playoffs). If people need some rest, they should get it. Going in healthy is important, but the games are important to win, too.”

Outfielder Jason Bay agreed. “We’re going out there still trying to win games, regardless of what’s at stake. A lot of it is out of our hands. Until it’s set in stone, it’s not set in stone. It’s highly unlikely, but we’re still going out there trying to win every game.”

The most impressive development coming out of this game was the pitching of Lester. He didn’t allow a hit over the first five innings, and kept the Indians off-balance with a mid-90s fastball and a sharp cutter. Lester’s perfect night cracked in the sixth when Josh Barfield led off with a double and Jamey Carroll hit an RBI single. But by then the Red Sox were ahead, 5-1, and Lester left after the sixth inning having thrown 86 pitches.

Even as he blanked the Indians, Lester said he didn’t think of a repeat of his season highlight: a no-hitter against Kansas City on May 19.

“It’s one of those things where if it happens it’s nice, but you know that we have to get ready for the playoffs,” he said. “We have to make sure that everything is healthy for then, and that’s all we can really worry about.”

Lester improved to 16-6 for the season and lowered his ERA to 3.21. He’s a sterling 11-1 at Fenway, a stat that will weigh heavily in the minds of Red Sox leaders when they line up the playoff pitching rotation.

“He really did well,” said manager Terry Francona. “He never had a real long inning. He did a good job.”

Instead of a full-force rush to the finish line, the Red Sox are using the final few games of the season to balance their pitching staff and get some rest for the regulars. David Ortiz sat last night, and Francona is promising Kevin Youkilis and Dustin Pedroia breathers soon, too.

In the meantime, the still-flickering hopes of a division title remain.

kmcnamar@projo.com