The Jays’ Alex Rios is forced out by Red Sox second baseman Dustin Pedroia, who fires to first to complete a seventh-inning double play.

AP / Chris Young

TORONTO –– The day began with more playoff-clinching scenarios than even the most interested observers could count.

What did the Red Sox need in order to clinch a postseason spot –– a win, plus a Yankee loss and a Tampa Bay win? Or was it a win, a Yankee loss and a White Sox loss? Or, was it either?

Did manager Terry Francona understand all the various points of playoff scenarios?

“Not as much as I probably should,” Francona said yesterday morning. “I figure if we win, we’ll probably be OK.”

By the second inning against the Toronto Blue Jays, it all became rather moot and the scoreboard watching ceased to matter, at least for the afternoon. The Sox had made the mistake of falling behind, 5-0. Worse, Toronto had Roy Halladay on the mound, a pitcher as likely to give up an early big lead as Francona was capable of grasping all the what-ifs surrounding his team’s potential playoff status.

As it happened, the Red Sox stayed close, with Jon Lester rebounding from two rough innings to toss five more shutout frames, while a run-scoring single from David Ortiz and Jason Bay’s two-run homer in the third helped the Sox briefly entertain comeback hopes.

But Halladay didn’t allow another run after Bay’s blast, and an eighth-inning homer by Scott Rolen off reliever Justin Masterson served to put an exclamation point on what would be a 6-3 Toronto triumph.

“You can’t spot a pitcher like Halladay a five-run lead in the second,” said Lester, “and hope to have a chance to win the game.”

Before and after the three-run third, the Sox had some chances against Halladay.

In the first, a leadoff single by Jacoby Ellsbury and a walk by Dustin Pedroia gave the Sox two on and none out. But even after both baserunners moved up with stolen bases, the Sox couldn’t deliver the runs, stranding both.

After two out in the fifth, the Sox used a walk to Ortiz, a single by Kevin Youkilis and a walk to Jed Lowrie to load the bases. But Halladay reared back to record one of only three strikeouts in the afternoon, fanning Lowrie to leave the bases full.

“We had some opportunities to do some things,” said Francona. “But (Halladay) is one of the best competitors in the league.”

Bay thought Halladay was less dominant than usual, but noted that the Toronto ace still found a way to win his 19th game of the season.

“Even on a day when he didn’t have his best stuff,” Bay said, “you know he’s going to be tough.”

The win may have been a serious blow to the Red Sox’ fading division title hopes. The Sox’ defeat, along with Tampa Bay’s win over Minnesota, dropped the Sox three games back in the loss column with only eight games remaining. Keeping in mind that the Rays will win any tiebreaker between the clubs, the Sox are staring at a significant deficit.

That was the case with Lester, too, who was nicked for a run in the second, then was racked for four more in the second.

For a brief time, in fact, the outing was starting to resemble Lester’s start last Aug. 23. In that game, Lester was shelled for eight hits and seven runs in just 2 1/3 innings, his most ineffective and truncated start of the season.

Yesterday, a two-run double by Marco Scutaro, a run-scoring single by Jose Batista and an errant throw home by shortstop Alex Cora, attempting to cut down Scutaro, produced the four runs.

“I made some pretty good pitches that they hit,” said Lester, “and I made some bad pitches they hit, too. I didn’t do a good job of keeping the ball game in control.”

Not in the first two innings, anyway. But thereafter, Lester kept the ball down and allowed just two more hits –– both singles –– the rest of the way.

“After the second,” said catcher Jason Varitek, “he was able to get his release back. We were able to expand the other side of the plate the rest of the way.”

In the eighth, with Halladay out and Brandon League in, the Sox presented themselves with one more shot. An infield single by Bay, coupled with a botched double-play effort by first baseman Lyle Overbay and a groundout gave the Sox the potential tying runs in scoring position.

Alex Cora then smoked a shot that seemed ticketed for center field, but League stabbed it with his glove, threw Cora out for the final out of the inning and effectively sealed the Jays’ win.

smcadam@projo.com