Kim gave up three pivotal home runs to the Yankees while pitching for Arizona in the 2001 World Series, which the Diamondbacks won in seven games.
This time, Green's homer came with a runner on and broke a 9-all tie. Moeller hit a solo shot.
Kim was charged with four runs in one inning while taking the loss.
It was the second time in less than a week that Kim allowed two homers to the Yankees in an inning. Last Thursday in Tampa, Cody Ransom and Robinson Cano connected off the sidearmer.
Kim, signed as a free agent on Feb. 24, has allowed five home runs in four innings this spring.
"He started later than everyone else and I think that has something to do with the way he's pitched," Pittsburgh manager John Russell said. "We'll keep running him out there and see if he gets better."
Kim wasn't the only pitcher to struggle on a windy night as both starters had rough outings and each team hit three home runs.
"It was tough conditions to pitch in," New York manager Joe Girardi said. "It was just one of those nights in Florida that you'll have sometimes. Some of their home runs probably wouldn't have gone out on a normal night and I think some of our home runs probably would have stayed in the park, too."
Yankees right-hander Phil Hughes allowed seven runs, six earned, and seven hits in four innings. Pittsburgh's Matt Morris was rocked for eight runs and 13 hits in four innings.
"I was over-striding, overthrowing a little bit," Hughes said. "I got frustrated when a couple of those balls left the yard. I tried to put a little extra on it and that just got me in more trouble."
Kei Igawa pitched one scoreless inning for the win.
Jorge Posada went 3-for-4 with three RBIs for the Yankees, including a two-run homer off Morris. Bobby Abreu added two hits and two RBIs.
Nate McLouth, Ryan Doumit and Chris Gomez homered for the Pirates.
Pittsburgh second baseman Freddy Sanchez saw his first action in the field this spring as he played the first five innings. He had shoulder surgery last September.
"The shoulder felt OK, but it's not where it needs to be yet," Sanchez said. "The good thing is there was no pain there, not even any discomfort. It's just a case of it not feeling as strong as it needs to be. The beauty of it is we still have time to get it right by opening day."
The first night game at McKechnie Field was originally scheduled for March 7 against Cincinnati but was rained out.
"It was a really neat atmosphere. The crowd was really into it," Sanchez said. "It was fun."
