Travis Hafner, Brett Gardner and Jayson Nix each homered off Darvish, who hasn't won in seven starts. Leonys Martin connected twice off Yankees starter Hiroki Kuroda.
Mariano Rivera (1-1) worked a scoreless ninth for New York, which ended the Rangers' five-game winning streak.
Scheppers (5-1) pitched a perfect eighth before being touched up by Suzuki in New York's first walk-off win this year.
ORIOLES 6, INDIANS 3: In Baltimore, Chris Davis and Alexi Casilla homered in a five-run seventh inning, and Baltimore ended a four-game losing streak.
Davis tied the game at 3 with his major league-leading 28th home run, a two-run shot, and Casilla added a three-run drive. Both homers were off Justin Masterson (9-6), who took a three-hitter into the seventh.
Chris Tillman (9-2) gave up three runs, four hits and four walks in seven innings to win his fifth straight start. The right-hander is 6-0 in seven starts since May 19.
Jim Johnson pitched the ninth for his 27th save.
Jason Kipnis homered, walked twice and singled for the Indians, who were seeking a fourth straight road victory for the first time since April 2012.
RAYS 5, JAYS 1: In Florida, Matt Moore overcame control problems to allow one run over six innings.
Moore (10-3) tied career highs with six walks and 11 strikeouts en route to his 10th win this season and second straight after a three-game skid. The left-hander gave up four hits.
Tampa Bay rookie Wil Myers had an RBI single during a three-run fourth. Considered one of baseball's top prospects, the outfielder has eight RBIs in nine games since being called up June 18 from Triple-A Durham.
Mark Buehrle (4-5) gave up four runs, eight hits and four walks in five innings for the Blue Jays, who have lost two in a row since arriving at Tropicana Field after tying a franchise record with 11 consecutive wins.
NATS 7, D-BACKS 5: In Washington, Adam LaRoche hit a three-run homer and Gio Gonzalez won for the first time since May 5.
Jayson Werth added a double, RBI-single and two walks for Washington, which led 6-0 after five innings and snapped a two-game skid.
Gonzalez (4-3) went 6 1-3 innings, giving up two runs on nine hits. He struck out four and walked one. Rafael Soriano allowed an RBI-single to Miguel Montero in the ninth, but picked up his 20th save.
Martin Prado homered and Paul Goldschmidt had three hits for Arizona. Diamondbacks second baseman Aaron Hill, playing his first game since going on the disabled list April 14 with a broken left hand, went 2 for 4 with a double, single and walk.
MARLINS 4, TWINS 2: In Miami, Marcell Ozuna drove in two runs and Derek Dietrich homered to help Miami over Minnesota Twins.
A.J. Ramos (2-2) pitched two scoreless innings in relief and Steve Cishek worked the ninth for his 13th save for the Marlins, who have won four of five.
Miami starter Jose Fernandez allowed one run and four hits in five innings. The 20-year-old phenom struck out three and walked three while throwing 94 pitches, 59 for strikes.
Fernandez is 2-1 with a 1.67 ERA in five June starts.
Kevin Correia (6-5) held the Marlins scoreless through five innings before running into trouble in the sixth.