Blalock, who also had a two-run homer, made a winner of Cordero (3-2), who allowed Oakland to tie the game with two runs in the top of the ninth.
It was Cordero's fourth blown save in seven opportunities this season.
"He's still one of the game's premier closers and we can't wait to give him the ball next time," Blalock said. "That's how we do it, as a team. If one guy has a bad day, we've got 24 other guys to pick him up.
"It's really exciting to see things like that, your teammates coming together. It was a big win for us."
Blalock was mobbed by celebrating teammates after the Rangers won for the fifth time in six games and ninth in 12.
The A's have lost 10 of 14.
Cordero allowed a leadoff single to Mark Kotsay in the ninth and walked Nick Swisher. After both runners moved up on a groundout, Kotsay scored from third on Frank Thomas' groundout. Dan Johnson's two-out double drove in Swisher with the tying run.
The Rangers' bullpen is 3-for-9 in save opportunities, and manager Buck Showalter is concerned.
"We are going to need to get it straightened out if we are going to get where we want to go this season," Showalter said. "If it's not something we can figure out, then we will have to come up with a solution."
Johnson game-tying double came on the pitch after he stepped out of the batter's box to collect himself after taking a 96 mph fastball from Cordero.
"I wanted to relax and focus on one pitch," Johnson said. "It was a fastball in and I put the right swing on it."
Blalock and Kevin Mench hit back-to-back homers in the third inning.
Blalock's two-run shot off the right field foul pole -- his fifth -- gave Texas a 3-0 lead. Mench followed with his fifth of the season, becoming the fourth player in Rangers history to homer in five straight games.
Nevin added a solo homer in the fifth off starter Barry Zito. Nevin's seventh homer of the season, and third hit of the game, extended Texas' lead to 5-1.
Rangers starter Vicente Padilla allowed three runs and six hits in 5 2/3 innings. He struck out three and walked four.
In his previous start against Oakland on April 15, Padilla became the first pitcher in major league history to allow homers on three consecutive pitches when Eric Chavez, Thomas and Milton Bradley all went deep in the sixth inning of the A's 5-4 victory.
Zito gave up five runs and six hits in six innings. He struck out five and walked four, leaving with his team behind, 5-3.
"I got out of some (jams) but I left a couple of pitches up and that can cost you the game," Zito said. "I'm frustrated with (my) up-down approach in April."
The Rangers loaded the bases with two outs in the first. Zito hit Mench on the arm with an inside pitch to force in the game's first run, then struck out Brad Wilkerson.
The Athletics made it 4-1 in the fifth on consecutive doubles by Jay Payton and Kotsay. They made it 5-3 in the sixth on a run-scoring single by Jason Kendall and a fielding error by second baseman D'Angelo Jimenez.
- Oakland has a team batting average of .225, last in the majors.
- The temperature was an unseasonably cool 62 degrees when the game got under way.
- Zito threw 30 pitches in the first inning.
- Carl Everett, Teixeira and Alex Rodriguez are the only other Rangers to homer in five straight games. Everett and Rodriguez accomplished the feat in 2003, Teixeira in 2004.
- Bradley left the game in the middle of the fourth after jamming his right knee when he slid back to first on a pickoff attempt. Bradley is day-to-day with a slightly sprained knee.