ARLINGTON, Texas (AP) -- Gary Matthews Jr. made sure nobody could rob him of this home run.
The Tigers had erased a four-run deficit before Matthews homered leading off the seventh against starter Jason Johnson (2-3).
"Gary picked a good time to hit his first homer," Rangers manager Buck Showalter said.
Matthews was robbed of a grand slam on May 3 at Oakland on Bobby Kielty's leaping catch, but this time the ball easily cleared the wall in right field.
"I finally got one out," said Matthews, who had 11 homers for the Rangers last season. "I had to hit it a few rows back so no one would catch it."
Cordero took the loss on Monday night when he gave up two runs in the ninth of the Tigers' 2-0 victory. This time, the relief corps came through, getting 3 1/3 scoreless innings from Brocail, Nick Regilio and Cordero.
"As a pitcher, you're going to go through some tough times," Cordero said. "You're going to give up some runs, and sometimes it'll be like tonight when it's 1-2-3."
Texas has won six of eight. Detroit had a three-game winning streak snapped.
Johnson allowed eight hits in Detroit's first complete game of the season. He struck out six and didn't issue a walk.
Rangers starter Chan Ho Park took a 4-0 lead into the sixth, but Texas couldn't hold it.
Park's five shutout innings extended the streak of scoreless innings by Texas starters to 27 over the last four games before Craig Monroe's RBI single in the sixth moved the Tigers within 4-1.
The 27-inning streak is the second longest in club history behind 35 in a row in 1981.
Park allowed four runs and eight hits over 5 2/3 innings, and the Tigers did much of their damage on two-strike counts. Park struck out five and walked one.
"He'd be the first to tell you that he made some mistakes on two-strike counts," Showalter said. "He had a lot of counts in his favor and couldn't finish off the hitters. But he pitched well and gave us a chance to win."
The Rangers took a 3-0 lead in the first on Blalock's two-run double and Alfonso Soriano's RBI double.
In the third, Blalock's sixth homer made it 4-0.
Johnson then got on track, retiring 11 of the next 12 before Matthews homered.
"Jason settled down to pitch great," Detroit manager Alan Trammell said. "They jumped on us early, but we came back and had our chances to win. I like that part."
The Tigers wasted a prime scoring chance in the eighth when they failed to score after putting runners on second and third with one out. Regilio struck out Inge and got Ivan Rodriguez on a fly out to end the threat.
"We had our opportunity there but we couldn't get that run in," Trammell said.
Carlos Guillen, who began the night as the AL's top hitter at .387, was the Tigers' DH after getting Monday night off to rest a swollen knee. Trammell said Guillen, who went 2-for-5 on Tuesday night, would probably be back at shortstop for Wednesday's game. ...The Rangers and Tigers conclude their three-game series on Wednesday and will end play against each other on June 2 in Detroit. That's the earliest point in Rangers history to complete a season series against an AL opponent. The six games between the teams are the fewest ever. ... The Rangers have one error in their last 13 games. ... Park and first baseman Mark Teixeira combined for a superb fielding play in the second on Ramon Martinez's line drive off Park's right leg. The ball popped into the air, Park grabbed it on the run with his bare hand about halfway between the mound and first and got off a low throw that was scooped by Teixeira to nip Martinez.