The mid-season addition blasted a 10th inning walk-off grand slam to beat Texas 4-0 on Sunday, giving Kansas City (82-73) their first winning season since 2003 and keeping them 3 1/2 games back of an AL Wild Card spot.
James Shields delivered in the Royals' attempt to capture the series, pitching eight shutout innings, giving up six hits while striking out two batters.
Rangers (84-71) starter Alexi Ogando matched him stride-for-stride, allowing zero runs through seven frames while recording five strikeouts.
Tim Collins (3-6) picked up the win after pitching a perfect 10th inning.
Kansas City begins the final week of the regular season Monday with the start of a three-game series at Seattle.