Dominic Leone gave up three runs in the sixth in his D-backs debut and the Mets added three more runs in the eighth and ninth.
"It's just tough, you know, [Leone's] just trying to impress his teammates and impress his new fans and probably trying a little too hard," D-backs manager Chip Hale said. "He'll get it. He's got a good arm."
"Everything was up," Leone said. "They put some good swings on some balls that they should've hit, and they did. They just made the best of the mistakes that I made."
In 10 relief appearances with the Mariners, Leone was 0-4 with a 6.35 ERA. Last season, the right-hander was 8-2 with a 2.17 ERA in 57 appearances.
Addison Reed had pitched well in his last few outings as he continued to work out the mechanical issues that cost him the closer's role in May. He had made five straight scoreless appearances spanning 5 2/3 innings before allowing a run in an inning on Thursday.
Before the bullpen's struggles, Ray threw five scoreless innings. In both the first and second innings, the left-hander allowed a runner to reach third with no outs. But each time, Ray retired three straight Mets to prevent a run from scoring and strand a pair of runners.
However, Arizona hasn't had a starter complete six innings in any of its last five games.
"Just a couple times I wasn't able to put away hitters and got deep in the counts," Ray said. "A couple times tonight I went 0-2, 1-2, and guys are battling. I'm just going to work on in my next bullpen just being able to put guys away."
Jake Rill is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.