The Rangers, who came from three runs behind to down the Mariners Tuesday, again rallied from a three-run deficit and tied the game in the fifth on Ian Kinsler's two-run homer.
Seattle then scored in the seventh off Koji Uehara (1-2), who was obtained by the Rangers in a trade with Baltimore last month. Mike Carp led off the seventh with a single and moved to second on a base hit by Franklin Gutierrez.
That brought up Wells, who singled to left on a 1-1 pitch to drive in the eventual winning run.
Texas put a runner on in the seventh, eighth and ninth and had the tying run on second with one away against closer Brandon League in the final inning. League got David Murphy on a fly ball to center and Kinsler on a grounder to third to end the game and pick up his 27th save.
Jason Vargas (7-10) worked seven innings to get the win, giving up three runs on six hits. He had gone six starts without a victory.