The tournament, the only one held on grass courts in North America, features a number of Olympians from 10 different countries scheduled to play before heading to the London Games on Wimbledon's grass surface later this summer.
Young, the 57th-ranked player in the world coming into the week, is part of the U.S. Olympic team.
Young dominated in the opening set, winning 10 of 11 first-serve points and 16 of 18 service points overall. He closed the set in 25 minutes before the 96th-ranked Russell changed his attack.
"It's difficult on a grass court, it's almost like you're hitting and you keep waiting to see who's going to get a bad bounce first," Russell said. "I thought I was playing a little more aggressive in the second or the third set. Even when I did miss, I thought I was playing with the right style of play."
In the final set, Young fought off three match points in the ninth game before Russell closed it out when Young hit a backhand service return into the net on the final point.
"Obviously I wanted to close it out when he was serving. But like I said, in the third set I felt really comfortable in my serve and was able to serve it out, which was nice," Russell said.
At one point during the second set when the chair overruled Mahut's serve, calling the ball in, Chiudinelli could easily be heard yelling, "You're making some of the worst calls here."
In other first-round play, American Jack Sock won his first ever match on grass, beating Russian Igor Kunitsyn 7-5, 1-6, 6-4; Belgian Olympian Olivier Rochus beat Japan's Go Soeda 6-4, 3-6, 6-3; and Israel's Dudi Sela beat Canadian Frank Dancevic 6-0, 6-2.
The tourney is held conjunction with induction ceremonies. Jennifer Capriati heads the 2012 class that will be enshrined on Saturday.