Monday they return to American League Central play against a Cleveland team trying to climb out of a rut in its quest to catch surprising division leader Detroit.
"Hopefully, this game makes us stronger and closer against our own division," Guillen said after the Sox cut Detroit's lead to 21/2 games, marking the first time since May 19 they gained ground in the division.
Guillen didn't shake up the lineup as he had threatened to the previous night after the Sox wasted a 14-hit attack and left 13 baserunners stranded. But center fielder Rob Mackowiak continued to make the most of his increased playing time with a solo homer in the eighth. He is batting .432 over the last 14 games.
"There's not one team that can run away with it," said right fielder Jermaine Dye, who hit a fifth-inning home run, his 13th, off Brian Tallet. "Detroit made some strides with the talent they got, changed the manager, and Jim Leyland has some guys playing well.
"We just can't worry about what other teams are doing. We just have to worry about here."
Aside from Juan Uribe failing to move a runner over on a bunt attempt in the second, the Sox responded well to Guillen's call for improved fundamentals. Shortly after Uribe's failed attempt, Alex Cintron delivered a two-out RBI single.
"The key is how each guy picks each other up," Guillen said.
Dye is batting .343 with five homers against lefties this season, but his homer was the lone run scored off Tallet and fellow left-hander Scott Schoeneweis in 41/3 innings. The Sox haven't fared as well against left-handers as they did last year, when they batted .271 against them.
The Sox face lefties Cliff Lee and C.C. Sabathia in the first two games of a four-game series starting Monday at Jacobs Field. In what could be his final chance, rookie Brian Anderson will return to the starting lineup despite batting only .122 (6-for-49) against left-handers.
"B.A. has to play," Guillen said. "It's not fair to Mackowiak (a left-handed hitter) to start against those lefties. I think Brian should have to be in the lineup against lefties, and [Tadahito] Iguchi in the second spot is pretty strong against lefties. We've got to stick with [Anderson]. We'll see what happens after the Cleveland series.
" If Brian continues to struggle, I will ask (general manager) Kenny Williams to see what we can do to get his swing back, or we will continue to play the way I'm playing him right now.
"I know there's pressure. But when you are struggling you need confidence, especially with him. When you have confidence, you will perform."
Jon Garland (4-2), who questioned his own confidence four starts ago, won for the second time in three starts and threw with more aggressiveness.
He was one out away from escaping danger through six innings when the Blue Jays cut the deficit to 6-4 on consecutive home runs by Troy Glaus and Lyle Overbay.
"I wasn't out there picking," said Garland, who was pulled after a leadoff double to Luis Figueroa in the seventh. "I was letting it fly."
Bobby Jenks converted his 14th save in 15 chances.