After Harvey exited, Robles (4-3) allowed a two-run double to Carlos Beltran and a three-run home run to Dustin Ackley to give the Yankees a 5-1 lead.
Harvey pitched five innings of one-hit ball, striking out seven batters and allowing one walk. Collins pulled Harvey to restrict his innings as the Mets (84-65) seek their first playoff berth since 2006 (Sept. 20). Harvey retired the last seven batters he faced and threw 51 of his 77 pitches for strikes.
Jacoby Ellsbury led off the sixth inning with an infield single and advanced to second on a Daniel Murphy throwing error. Brett Gardner then bunted back to Robles, whose throw to David Wright was dropped.
Beltran then lined a two-run double to centerfield and four batters later, Ackley homered into the right-centerfield bullpen that made it 5-1.
The Mets' bullpen continued to struggle after Robles left. After Eric O'Flaherty loaded the bases in the seventh inning, Erik Goeddel walked Chase Headley to make it 6-1.
Carlos Torres and Tim Stauffer combined to allow five runs in the eighth inning, capped by Greg Bird's three-run home run that made it 11-1.
CC Sabathia struck out seven batters and allowed five hits in six innings for the Yankees (82-66).
Sabathia (5-9) settled down after a 32-pitch first inning in which he allowed back-to-back doubles to Ruben Tejada and Wright that gave the Mets an early 1-0 lead.
The Mets loaded the bases with two outs, but Michael Cuddyer fouled out to first.
Murphy hit an RBI single in the eighth inning.
The Mets begin a three-game home series with the Atlanta Braves on Monday.
Jon Niese (8-10, 4.31 ERA) will face Shelby Miller (5-15, 3.00 ERA) at 7:10 p.m.