After losing the opening game of the series, Oakland has won two straight to move within three games of Texas for the lead in the American League West. The teams will face each other again on Thursday and then finish the season with three meetings in Oakland.
The Rangers sent recent call-up Martin Perez (1-3) to the mound for the fifth time in his career and he recorded only two outs while the Athletics were quickly taking charge.
Stephen Drew opened the game with a double and scored on a one-out triple by Cespedes.
Cespedes came in on a single by Chris Carter, Brandon Moss delivered a base hit and Josh Donaldson singled as well. Carter and Moss both scored when Texas center-fielder Josh Hamilton misplayed Donaldson's hit.
The triple by Norris brought home Donaldson with the final run of the inning. Norris also singled in a run in the fourth and had a sacrifice fly in the ninth.
Jarrod Parker (12-8) collected the win, allowing five hits and three runs with eight strikeouts in six innings.