Querrey, the runner-up at the 2009 Newport event, was upended by Smyczek 6-4, 7-6 (10-8) at the International Tennis Hall of Fame and Museum.
The news was better for fourth-seeded 2012 runner-up Lleyton Hewitt, however, as the Australian overmatched compatriot Matthew Ebden 6-4, 6-1.
Hewitt fell in last year's final to two-time defending champ John Isner, seeded second in this year's edition.
Also advancing to the second round Tuesday were No. 2 seed Igor Sijsling of the Netherlands, who dispatched Italian Matteo Viola 6-4, 6-1, and eighth-seeded American Rajeev Ram, who breezed past Swiss qualifier Adrien Bossel 6-2, 6-2.
Elsewhere at Newport, fifth-seeded Frenchman Edouard Roger- Vasselin was upended by Croatia's Ivo Karlovic and American Jack Sock downed sixth-seeded Australian Marinko Matosevic, 6-2, retired.
Americans Michael Russell and Alex Kuzentsov, France's Nicolas Mahut, Indian wild card Prakash Amritraj, Canadian Vasek Pospisil and Czech Jan Hernych also moved into the second round with Tuesday victories.