Guillen also hit a solo homer for Detroit, which hadn't won 12 in a row since 1934-when Hank Greenberg, Charlie Gehringer and the Tigers lost a seven-game World Series to the St. Louis Cardinals' famous Gas House Gang.
Jose Valverde finished up in the 10th to remain perfect in 44 save opportunities this year.
Closing in on an AL Central title, the surging Tigers rallied for three runs in the ninth off Chicago's bullpen to prevent rookie Dylan Axelrod from earning his first career win.
The Tigers have won 22 of their last 26 games overall and 21 of 27 against the White Sox.
Santos (4-5) blew his sixth save of the season.
In Boston, the reeling Red Sox lost for the sixth time in seven games, wasting an eighth-inning lead when Adam Loewen's two-run single off Daniel Bard lifted the Blue Jays.
Just 3-10 in September, the Red Sox began the day with a four-game lead over Tampa Bay in the AL wild-card race. Boston led the AL East at the start of the month and was nine games ahead of the third-place Rays.
After getting swept in a three-game series at Tampa Bay last weekend, Boston hosts the Rays in a four-game series starting Thursday night.
Boston led 4-2 in the eighth before Toronto came back against the hard-throwing Bard (2-8).
Ricky Romero (15-10) allowed four runs-three earned-and six hits in eight innings. He improved to 8-1 in his last 10 starts.
In Oakland, California, Jered Weaver went seven innings for his career-best 17th win, Mark Trumbo hit a tiebreaking homer in the sixth and the Angels beat the Athletics.
Bobby Abreu added two hits and scored twice for the Angels, who began the day three games behind first-place Texas in the AL West. The Rangers were set to host Cleveland at night.
Josh Willingham matched his career high of 26 home runs with a solo shot off Weaver in the third but the A's managed only two base runners over the final six innings.
Weaver (17-7) allowed six hits with one walk and two strikeouts. He pitched out of a bases-loaded situation in the first and escaped a two-on, one-out jam in the second to beat the A's for the third time in four starts this season.
Rich Harden (4-3) didn't make it out of the sixth, allowing three runs and seven hits.
In Kansas City, Mike Moustakas had three hits and drove in two runs and Luke Hochevar pitched six solid innings to help the Royals beat the Twins.
The Royals have won four straight, matching the longest winning streak of the season, while the Twins have lost 19 of 23 and are in last place in the AL Central after winning the division the past two years.
Hochevar (11-11) gave up two runs on five hits in six innings.
Liam Hendricks (0-2), who was making his second big league, was roughed up for five runs on eight hits in five innings.
In Arlington, Texas, Josh Hamilton's third career grand slam highlighted an eight-run fourth and Derek Holland pitched seven effective innings as the Rangers beat the Indians.
Hamilton's 21st homer and Mike Napoli's 26th were the key blows off rookie David Huff (2-5) in the decisive fourth, Texas' biggest inning since an 11-run fifth against Tampa Bay on Sept. 26, 2009.
Holland (14-5) allowed one run and six hits with six strikeouts and three walks. He has won eight of his last nine decisions, a stretch that began on July 7.
Ian Kinsler also homered for the AL West-leading Rangers, who have won three straight and maintained a three-game lead over second-place Los Angeles, which beat Oakland 4-1 Wednesday.
Baltimore, the Rays missed an opportunity to gain ground in the wild-card race, getting only three hits over seven innings against Jeremy Guthrie in a loss to the Orioles.
After watching Boston lose to Toronto in an afternoon game, the Rays took the field with a chance to close within three games of the Red Sox in the AL wild-card hunt.
Instead, Tampa Bay lost its second straight to the last-place Orioles.
Next up for the Rays: Four games against the Red Sox at Fenway Park, beginning Thursday night. Tampa Bay swept a three-game series from Boston last weekend and is 9-5 against the Red Sox, including 4-1 on the road.
Seattle, Luis Rodriguez led off the bottom of the 12th inning with a solo homer off New York reliever Cory Wade, and the Mariners delayed Mariano Rivera's chase for the saves record.
Rodriguez, who doubled in his previous two at-bats, golfed a 2-1 pitch from Wade (5-1) into the right field seats and sent the Yankees off to Toronto looking to get Rivera career save No. 601 on Friday night against the Blue Jays.
Seattle reliever Steve Delabar (1-0), who was a substitute teacher earlier during the baseball season before being signed by the Mariners, earned his first major league victory.
