The Rangers avoided a three-game sweep at the hands of the Mariners, who owned a 3-1 lead heading into the bottom of the seventh.
Texas had scored just five runs in the first 24 innings of the series before sending eight men to the plate in the seventh.
Charlie Furbush relieved Iwakuma, but surrendered an RBI single to Mitch Moreland and a sacrifice fly to Elvis Andrus that brought in the go-ahead run. A fielding error by second baseman Nick Franklin allowed Leonys Martin to reach base and Ian Kinsler then drove in a run with a single.
Josh Lindblom (1-2), the fourth of six Texas pitchers, recorded the final two outs in the top of the seventh to get the win. Lindblom came on after Ibanez had hit a two-run homer that gave the Mariners a two-run lead.