Cabrera (1-0) was pulled after giving up a a leadoff homer to Chad Moeller in the seventh. The right-hander allowed two runs, five hits and a season-low two walks.
Nick Markakis opened the sixth with a single, and Kevin Millar singled before Luke Scott singled in the go-ahead run. After Aubrey Huff popped out, Adam Jones chased Hughes with an infield hit that drove in another run. Former Oriole LaTroy Hawkins issued an intentional walk before Payton drove in two runs with a pinch-single.
Brian Roberts then grounded out, but Mora ended Hawkins' outing with a two-run single. Markakis followed with his second hit of the inning, an RBI single off Edwar Ramirez.
Hughes (0-3) gave up five runs and a career-high eight hits in his 17th major league appearance. It's also the first time in his professional career he has lost three straight starts.
New York missed a chance to break a scoreless tie in the fourth inning when Markakis threw out Bobby Abreu trying to score from second on a two-out single to right by Hideki Matsui. Scott doubled and scored on a double-play grounder in the bottom half.
The Yankees tied it in the fifth when Robinson Cano singled, took third on Melky Cabrera's double and scored when Mora booted Moeller's grounder to third. With runners on the corners and two outs, Derek Jeter grounded out.
After two walks and a hit batter loaded the bases for New York with two outs in the sixth, Daniel Cabrera pumped his fist and screamed with delight when he struck out Melky Cabrera on a 2-2 pitch.
Baltimore ended all the suspense in the bottom half.