With Edwin Nunez at the plate, Wells went to second when Nathan slipped off the mound while delivering a pitch and Nunez followed by smacking a score-tying triple off the base of the centerfield wall.
That brought up Lillibridge, who lined a solid hit to left for the decisive blow as Nathan blew just his second save opportunity of the season.
Lillibridge finished with two RBI while Ichiro Suzuki and Austin Romine each drove in a run for the Yankees, who broke a two-game skid.
Mitch Moreland smacked a two-run homer for Texas.
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