Henn, the seventh New York pitcher of the evening, opened the 11th by striking out Curtis Granderson but issued a full-count walk to Placido Polanco.
Polanco was picked off by catcher Jose Molina, but Sean Casey singled to center and Magglio Ordonez dropped a single into shallow right. Guillen followed by blasting a 1-2 slider over the left-field wall for his 18th home run.
"I thought it was a decent pitch when it left my hand," Henn said. "He must have, too."
The marathon affair of four hours and 24 minutes followed a rain delay of four hours and one minute, during which the playing field was pelted with torrential downpours and a tornado warning was issued for the area. No official records are kept on the length of rain delays.
The Yankees said they received back-and-forth reports on the delay and estimated start times, though it was the duration of the evening that weighed upon them heaviest.
"It certainly made it tougher to lose," said Yankees manager Joe Torre. "I don't know what to say. We're pretty well spent right now."
The Yankees had their best chance to regain the lead in the ninth inning against Fernando Rodney, as Melky Cabrera singled and stole second on a Derek Jeter strikeout. But Alex Rodriguez also fanned and Jorge Posada went down looking to end the inning before being ejected -- at 2:25 a.m. ET -- by home-plate umpire Bob Davidson.
"That strike zone was a mystery tonight, on both sides," Torre said. "When you start throwing out players in a pennant race, that really becomes a problem."
"I have nothing to say about that," Posada said.
The Yankees' missed opportunity, though, briefly paled in comparison to the Tigers' blown chance against Mariano Rivera in the 10th. Ordonez ripped the eighth pitch of his at-bat up the gap in left-center field and moved to third on a groundout, putting the winning run 90 feet away.
After the Yankees loaded the bases with two intentional walks, first baseman Andy Phillips made a great stab on a Brandon Inge liner, pinning the runners, and Cameron Maybin struck out swinging to end the inning, keeping the game rolling on.
Earlier, Edwar Ramirez had pitched a scoreless sixth and Joba Chamberlain retired the Tigers in order in the seventh before Kyle Farnsworth followed suit in the eighth. Luis Vizcaino allowed two baserunners in the ninth but got Casey to fly out, sending the game to extra innings.
"We pitched like [heck] out of the bullpen," Torre said. "They really did a great job."
Neither starter pitched particularly effectively. Behind Rodriguez's 43rd home run, a two-run shot in the third inning, the Yankees touched left-hander Andrew Miller for six runs and seven hits over 4 1/3 innings.
New York scored three times in the fifth to tie the game, with Posada drilling a two-run double and Hideki Matsui greeting reliever Tim Byrdak with an RBI single.
"It's tough when you score six runs," Posada said. "We had a pretty good chance to make a comeback."
Coming off victories in his last two starts, Roger Clemens wasn't at his sharpest, either. Ordonez reached Clemens for his 25th home run in the first inning, a line-drive, two-run shot over the wall in left field.
"You could tell, the first couple of innings, that it was going to be a game where our guys were going to score," Clemens said, "if I could just get command and get control of what I was doing out there."
Granderson drove in three runs on a pair of triples, driving in one in the third and two in the fourth, part of a four-hit night for the Detroit leadoff hitter.
"It just looked like he was fighting it," Torre said of Clemens, who walked three and struck out three over five innings. "He didn't look like he could locate. He had trouble getting balls down."
The Yankees used all but one of their position players, utility man Wilson Betemit, and all but one of their relievers, Brian Bruney, who was recalled from Triple-A Scranton/Wilkes-Barre earlier in the afternoon.
The defeat in the wee hours of the Detroit night pushed the Yankees 6 1/2 games behind the Red Sox in the AL East, while moving New York three games behind Seattle for the AL Wild Card.
"They get the last at-bat," Posada said. "When you're at home, it's a different ballgame.""
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.