"We came back, and we had it, man," Rangers manager Ron Washington said. "We just didn't get the hit. We had the right people up there. We just got beat. In the last two games, we were one hit away from the game being different. Today, we were one hit away from the game being different on three different occasions.
"We just couldn't get the knock."
Texas, which despite the sweep remained in first place in the American League West, lost its club-record 11th straight game at Comerica Park.
The Rangers also were swept in a three-game set at Comerica Park in April.
"It's not like we're getting blown out every game," Texas starter Kevin Millwood said. "We're playing good baseball. We're just coming out on the short end. It's a good thing we don't have to come back here."
The Rangers' offense struggled to find knockout punches throughout the series.
They went 3-for-17 with runners in scoring position and stranded 19 runners, including nine in Thursday's finale. Texas scored an uncharacteristic six runs in three games.
"Our pitching and defense are still solid," third baseman Michael Young said. "The guys did a good job on the mound. We picked them up defensively. We have to make a couple of adjustments offensively right now.
"The strength of this club is we make quick adjustments when it comes to hitting and turning things around."
Down two runs in the eighth, Hank Blalock's double to right gave Texas runners on second and third with one out. Detroit starter Edwin Jackson got Marlon Byrd to pop-out to short, but he couldn't retire the next batter, Nelson Cruz.
Cruz drove a two-strike fastball into the left-center gap for a two-run double to tie the game at three.
Detroit answered with the game-winning run. Placido Polanco lined a two-out single to center and moved to second after Clete Thomas walked. Cabrera knocked a first-pitch single to center, scoring Polanco and completing the sweep.
"I think he wanted to be aggressive with me," said Cabrera, who has hit .435 (10-for-23) against Texas this season. "He threw me a first pitch fastball up and in. I tried to put the ball in play."
Millwood wanted Cabrera to chase a pitch out of the strike zone, but the Tigers' first baseman smacked it to the outfield anyway.
"I thought I made a good pitch," Millwood said. "I was trying to get it off the barrel, and I was able to do that. He didn't barrel it up. He's just a great hitter and muscled it into center field."
Millwood allowed four runs on six hits in eight innings. He gave up a solo home run to Thomas and a two-run shot to Curtis Granderson that gave Detroit a 3-1 lead. This after not allowing a homer in his past two starts.
He dueled with Jackson, who came into the game sporting the second-best ERA in the AL. The two starters combined for 253 pitches.
Jackson completed a dominant trifecta by Detroit's starting pitching. Dontrelle Willis shutout the Rangers on one hit in the opener, red-hot Justin Verlander allowed one run on three hits and Jackson finished the hat trick with three runs in eight innings.
"We ran into some good pitching," Millwood said. "When you run into good pitching, it'll stop good hitting just about every time."
The Rangers loaded the bases with one out in the second. Elvis Andrus hit a fly ball that appeared deep enough to score a run, but Thomas fired a laser to catcher Dane Sardinha, who applied the tag on Cruz to complete an inning-ending double play.
In the fifth, the Rangers executed a double steal to put runners at second and third with two outs. But Young, one of the top hitters in baseball this month, couldn't drive them in.
The Rangers put a runner on third in the ninth against Tigers closer Fernando Rodney, but like too many other times in this series, they couldn't find a key hit. Young hit into a game-ending double play.
"We just couldn't get it done," Washington said. "That's been our forte this whole series. We just couldn't get that one hit we needed."