Now the question is whether Gavin Floyd indeed will make the All-Star team after throwing 71/3 shutout innings and raising his record to 10-4 with a 6-1 victory over Oakland before a crowd of 35,586 at U.S. Cellular Field.
Floyd is well aware he has a chance to be one of a very few Sox at Yankee Stadium in 10 days and says "if it happens great and if not, then I'll just try to keep on giving our team a chance to win.
"The whole goal this season is to make the playoffs and World Series and that's all we're really worried about. [Making the All-Star team] is kind of a plus if it happens."
Without Floyd pitching a gem, the Sox now would be tied for first with the Twins, who have won 15 of their last 17 games.
"We're just going to keep on focusing on what we can do," he said. "They're playing great and we are, too, so we just have to keep winning series."
And taking care of business.
"The Twins are hot," said Nick Swisher, who began the scoring with his 12th home run, "but we have to worry about what's going on on the South Side."
With his offense supplying power from Swisher, Brian Anderson and Alexei Ramirez, Floyd did his part by lowering his ERA to 3.22.
Floyd, who has lost only once in his last eight starts, got his first four outs on strikeouts and then survived constant trouble.
The A's had the leadoff hitter on base with a walk in the third and with singles in the fourth and fifth innings. But the only runner to reach third base was ex-Sox Ryan Sweeney in the sixth, when he walked and moved up on a wild pitch and ground out.
Is Floyd aware of his ever-increasing numbers?
"I'm conscious of it but every game you can't really control," he said. "You make pitches and try to control that and everything else kind of is out of your control."
Swisher put the Sox up 1-0 over his old teammates in the second with a towering homer to left field.
They were back for two more runs in the fifth inning when Orlando Cabrera led off with a single and Anderson walloped a 410-foot shot into the bleachers for all the runs they would need.
The victory over Greg Smith made the Sox 20-12 against left-handed starters, compared to 16-28 last season.
And an even more impressive number: The Sox are 46-16 when one of them hits a home run, a stat that also could earn Carlos Quentin and Jermaine Dye reserve All-Star berths.
"At least we hit them when we need it," Guillen said. "It seems like every time we hit a home run it puts us back in the game or we take the lead and that's a good thing."