The Rangers were clinging to a 2-1 lead in the eighth, but they sent 11 men to the plate against three pitcher in that inning.
Josh Hamilton, who hit his major league-leading 42nd homer of the season during the third inning, doubled home Andrus with the first run of the eighth.
Another run scored on a Seattle error, Geovany Soto doubled home two runs and Andrus then cleared the bases with his triple to right.
The Texas outburst overshadowed a two-hit, one-run effort by Yu Darvish (15-9), who struck out nine over seven innings to win his third straight decision.
Hisashi Iwakuma (6-5) gave up solo homers to Ian Kinsler and Hamilton over 5 1/3 innings and took the loss. He trailed by only one run when he left the game.