Robles, promoted this week when Jerry Blevins suffered a fractured left forearm, stranded the bases loaded in the seventh inning at Yankee Stadium.
After inheriting two baserunners with none out from Sean Gilmartin, the hard-throwing Robles allowed an infield single to Alex Rodriguez. Robles then coaxed a foul popout from Mark Teixeira and consecutively struck out Brian McCann and Carlos Beltran.
"I'm really happy about it," Robles said through an interpreter.
As for the first major league batter he faced being A-Rod, Robles added: "It was interesting, and I was really happy to face a player like Alex Rodriguez."
Robles, 24, had tossed 7 2/3 scoreless innings this season with Triple-A Las Vegas. He allowed six hits and one walk while striking out 10.
Robles twice has been on the Mets' 40-man roster. He was removed and cleared waivers on Nov. 22, 2013.
Robles then stumbled as a starting pitcher to begin the 2014 season at Double-A Binghamton. He had a 4.86 ERA in 18 starts through July 13.
The Mets converted Robles to relief at that point and he took off. He had a 1.80 ERA and .159 opponents batting average in 20 innings out of the bullpen the remainder of that season with the B-Mets. Robles then went to winter ball with Licey in his native Dominican Republic and continued to open eyes in October and November. He posted a 0.77 ERA in 13 relief appearances while registering in the upper 90s with his fastball.
The success out of the bullpen prompted the Mets to return him to the 40-man roster to shield him from December's Rule 5 draft.
Mets manager Terry Collins has told Robles he is "proud" of how the right-hander persevered after originally getting dumped from the 40-man roster. Collins said Robles' work ethic was tremendously improved this spring training.
"I think I took being taken off the 40-man as a challenge and I kept working, working, working until I got back again," Robles said.