The 11-run inning was an embarrasing moment in an already trying season for the Rangers, who's record fell to 7-15.
"Any time a team is in a losing streak, the manager's job is on the line," Washington said. "It falls on me when the team isn't playing well. I'm the manager ... that's the way it goes."
Jacque Jones also homered as Detroit scored its most runs this season. The Tigers, who lost their first seven games and were 2-10, are now 9-13 and moved out of last place for the first time this season in the AL Central, percentage points ahead of Cleveland.
"It's coming along good. Very positive for us," Ivan Rodriguez said. "It's a lineup, from 1-9, we can hit."
The Tigers led 7-6 going into the sixth, when they had their biggest inning since scoring 11 in the sixth inning on April 23, 2004, against the Cleveland Indians.
Wes Littleton relieved and gave up the final six runs in the innings, hitting Ramon Santiago with the bases loaded for his first run. Curtis Granderson doubled in two more, Rodriguez hit a run-scoring double, Guillen had a sacrifice fly and Ordonez singled in the final run of the inning.
"I think it was a combination of real good hitting and a couple of bad pitches for their team," Detroit manager Jim Leyland said. "But the biggest thing was walks."
Three of the 10 walks and both of the hit batsmen that Texas pitching surrendered came in the sixth.
"Our pitchers took a serious beating tonight," Washington said. "They threw too many pitches over the plate and they were hit hard."
The last time the Rangers gave up so many runs in an inning was also against the Tigers. Texas allowed 13 to Detroit in the ninth inning in Arlington on Aug. 8, 2001, in a 19-6 loss. Rodriguez was the Rangers' catcher in that game.
Clay Rapada (2-0) pitched 1 2/3 perfect innings in relief, striking out two.
Frank Francisco (0-1) allowed two runs in 2 1/3 innings of relief.
Both starters were ineffective.
The Tigers' Kenny Rogers allowed six runs and nine hits in 3 1-3 innings and saw his ERA rise to 7.66. Texas' Luis Mendoza didn't make it out of the second, giving up five runs -- two earned -- and five hits in 1 2/3 innings.
"I wasn't comfortable out there. My arm felt very weak. It has been that way for the last couple of outings," Mendoza said. "I feel OK when I warm up but after the first inning I feel the weakness in my arm. ... I'm concerned because I have never been injured."
Texas led 5-0 going into the bottom of the second, but Detroit scored five times in their half of the second.
"We've got a pretty good lineup, but getting down 5-0, you have to play nine innings every day," Guillen said. "Got to play consistent every game."
Granderson was 2-for-4, scored three runs and drove in two in his season debut. Detroit's centerfielder and leadoff man missed the first 21 games with a broken finger sustained during spring training. ... Jason Jennings, who was scheduled to pitch on Thursday for Texas, was moved back to Saturday. Scott Feldman, who will be recalled from Triple-A Oklahoma City on Thursday, will take his place. Kevin Millwood will still starts Friday and Jennings will replace Kason Gabbard in the rotation on Saturday. ... Tigers second baseman Placido Polanco, who missed the last five games with a sore back, is expected to return on Thursday and DH Gary Sheffield, who didn't play in the last four games because of a sore shoulder, could be back on Friday.