Russia's Evgeny Donskoy defeated Tiafoe, the world's seventh-ranked junior player and a D.C.-area native, 6-4, 6-4.
Top-seeded Tomas Berdych will face Ginepri, who advanced to the second round with a 6-4, 6-2 victory over Alejandro Falla of Colombia 6-4, 6-2. Young beat Yuichi Sugita of Japan 6-4, 4-6, 6-4.
American Shelby Rogers upset No. 3 seed Alize Cornet of France 7-5, 4-6, 6-4 in the WTA draw. No. 7 Madison Keys lost in straight sets while Svetlana Kuznetsova of Russia, the sixth seed, won 6-3, 6-2 over Slovenia's Polona Hercog.
Tiafoe trains at the tennis center in the Maryland suburbs where his father once worked as a maintenance man and the family occasionally lived. This year the 6-foot-1 slugger played boys' singles at the French Open, where he was the top seed, and at Wimbledon.
Donskoy, ranked 111 on the ATP tour, fended off enough forehand winners from Tiafoe and possible momentum-altering roars from the partisan crowd to break the local favorite twice in the final set.
''Tonight was probably the most fun I've ever had playing tennis,'' an upbeat Tiafoe said following the match. ''The whole crowd with you. Every point you win everyone is going crazy.
''It was really special playing tonight and I hope I can play here again for many years to come.''
Tiafoe, who received a wild card entry into the main draw, beat back three match points before eventually falling.
''This guy is just outside the Top 100 and we played a pretty competitive match tonight,'' Tiafoe said. ''At 16 and playing at the level like this, I leave here with confidence.''
John Isner received a first-round bye, as did Wimbledon semifinalist Milos Raonic of Canada. Isner, a finalist in Washington last year, won the Atlanta title on Sunday.
Other ATP winners on Monday included Americans Tim Smyczek and Rajeev Ram, and Australia's Bernard Tomic.
Taylor Townsend, the 18-year-old American qualifier, rallied for a 3-6, 6-2, 6-3 victory over Julia Goerges of Germany.