Borbon and Andrus each drove in a run and scored with two outs as the Rangers broke open a 1-1 tie and took their third straight from New York in Arlington, Texas.
Cliff Lee (11-8) was the beneficiary, collecting the victory after skipping a start to rest his back. The veteran left-hander responded well to the time off, holding New York to one run on two hits and three walks over eight-plus innings.
Neftali Feliz notched his 36th save in the ninth, striking out the side after Lee opened the frame by walking Derek Jeter.
Dustin Moseley (4-3) allowed four runs on five hits and two walks in 6 2/3 innings for the Yanks, who were swept in a three-game series for the first time this season.
New York, however, maintained its half-game lead over second-place Tampa Bay in the American League East.