The Yankees owned a 4-1 lead heading into the ninth and CC Sabathia stayed in the game in hopes of going the distance for the third time this season.
Alex Gordon, however, singled with one out and went to second on a single by Mike Aviles.
Aviles was erased at second on a fielder's choice grounder from Mitch Maier, but with Sabathia needing only one more out to end the game he was replaced by Robertson.
Robertson promptly gave up a two-run double by Willie Bloomquist, who then moved to third on an infield single by Wilson Betemit.
That brought up Kendall, who fouled off three pitches before swinging and missing on a 2-2 offering.
Sabathia (15-5) was charged with three runs on 10 hits. Robertson collected his first save of the season and the second of his career.
New York closer Mariano Rivera was not used because he had pitched the two previous nights against Texas.
Austin Kearns paced the New York offense with two hits, one of them a solo homer.
Bruce Chen (7-6) took the loss, giving up four runs on eight hits in five innings.