Blackley (6-4) stifled the Rangers on one run, yielding three hits and a pair of walks while striking out five for the playoff-bound A's.
Sean Doolittle and Ryan Cook each turned in a scoreless relief frame and Grant Balfour nailed down his 24th save as the Athletics pulled into a flat-footed tie with the Texas atop the AL West with their fifth straight win.
The two teams will meet in the final regular-season contest Wednesday to decide the division championship.
Jonny Gomes belted a solo homer and Derek Norris added an RBI for Oakland, which clinched a post-season berth Monday.
Texas starter Matt Harrison (18-11) absorbed the loss, surrendering three runs on six hits over six complete innings.
Josh Hamilton got the only RBI for the Rangers, who lost for the eighth time in 12 games.
They would settle for the AL's second wild card spot should they fall to Oakland in the final game.