Buehrle was beaten despite giving up just three hits over seven innings, and the White Sox fell to 0-4 this year against their Central division rival — scoring a total of three runs in the process.
Blackburn (6-4) matched his career high by winning his fifth straight decision, coming over his past nine starts.
He scattered seven hits, continuing a remarkable run this month by the Twins' rotation. Minnesota has won 11 of its last 13 games.
Buehrle (6-5) has pitched well over his last eight starts since the beginning of May, surrendering only 17 runs in 55 innings for a 2.78 ERA.
At New York, journeyman Brian Gordon kept the Yankees close in a most unlikely start, then Brett Gardner hit a winning single in the 12th inning that lifted New York to a three-game sweep.
The Yankees became the first team to sweep AL champion Texas this year. New York won for the sixth time in seven tries and sent the Rangers to their season-worst fifth loss in a row.
Gordon signed with the Yankees this week and pitched effectively, allowing two runs on seven hits in 5 1-3 innings. Cory Wade (1-0), who also signed with the Yankees this week, pitched two perfect innings for the win.
Gardner's one-out hit in the 12th came off Michael Kirkman (1-1).
At Detroit, Jhonny Peralta and Ryan Raburn hit back-to-back, solo homers in the fourth inning, Detroit moved a game ahead of Cleveland for first place in the AL Central.
The Tigers won twice in the three-game series, giving them 13 wins in 18 games. The Indians, on the other hand, have dropped 16 of 22.
Max Scherzer (9-3) gave up two runs and four hits, and hit two batters over 5 2-3 innings for Detroit.
Mitch Talbot (2-4) allowed six runs on nine hits over four innings.
At Toronto, Jeremy Guthrie pitched five shutout innings before a strained back forced him to leave the game, and Baltimore scored two runs in the ninth for the win.
Vladimir Guerrero and Luke Scott opened the ninth with back-to-back singles against Toronto closer Jon Rauch (2-3). Derek Lee followed with a swinging bunt that Blue Jays third baseman Jayson Nix charged on, but Nix's throw home was high, allowing pinch-runner Nolan Reimold to score for a 3-2 Orioles lead. Ryan Adams later added an RBI single.
Adam Lind's solo home run off Kevin Gregg in the bottom of the ninth made it 4-3, but the former Toronto closer recovered to earn his 13th save as Baltimore avoided a sweep.
At Oakland, California, Jemile Weeks had two hits and drove in three runs, and Hideki Matsui homered to lead Oakland past Kansas City.
Matsui's solo shot gives him a combined 499 homers in Japan and the US and helped Oakland win a second straight game for the first time since a four-game streak May 26-29.
Melky Cabrera had two hits and drove in a run for the Royals, who lost their second straight. Jeff Francoeur, Wilson Betemit and Brayan Pena each added an RBI.
Daric Barton drove in two runs, and Coco Crisp and Kurt Suzuki each had an RBI in support of Gio Gonzalez (6-5), who allowed two runs on five hits over six innings.
At St. Petersburg, Florida, Adrian Gonzalez homered and David Ortiz, Darnell McDonald and Dustin Pedroia drove in runs to back Clay Buchholz as Boston downed Tampa Bay.
The win was the 11th in 12 games for the AL East leaders, who concluded a 10-day, nine-game trip with an 8-1 record - Boston's best mark on a trip of at least nine games since 1977.
Buchholz (6-3) allowed one run and two hits in five innings before leaving the game because of lower back tightness. Tampa Bay trimmed a 3-1 deficit to one run on Casey Kotchman's solo homer off Alfredo Aceves in the sixth.
Gonzalez's solo shot off Kyle Farnsworth restored a two-run lead in the ninth.
Boston reliever Daniel Bard retired all four batters he faced and closer Jonathan Papelbon worked through a ninth-inning jam to earn his 13th save in 14 opportunities.
