Fifth seed Verdasco put up little resistance against Germany's Julian Reister, losing 6-2 6-3, while eighth-seeded Troicki crashed in three sets against Rafael Nadal's Wimbledon slayer Lukas Rosol, 5-7 6-3 6-4.
Seventh seed Florian Mayer of Germany was pushed hard as he beat Horacio Zeballos of Argentina 7-6(7) 7-5.
Spain's Albert Ramos beat compatriot Pablo Andujar 6-1 6-4 while Jeremy Chardy of France triumphed over Albert Montanes of Spain 6-4 6-2.
Tommy Haas set a second-round clash with second seed Gilles Simon after beating Martin Klizan 6-2 6-1 in 68 minutes.
Feliciano Lopez survived a scare in coming through his opening match at ATP Gstaad.
The Spanish fifth seed lost the opening set against world number 102 Adrian Ungur, but fought his way back into the match by taking the second.
He was then pushed to a nail-biting tie-break in the third set before closing out a 2-6 6-4 7-6(7) victory.
One seed who did drop out was sixth seed Julien Benneteau who was beaten by Bulgarian prospect Grigor Dimitrov 3-6 6-4 6-1.
Poland's Lukasz Kubot also struggled to get past Croatia's Ivan Dodig 3-6 6-3 6-4, but Brazil's Thomaz Bellucci had a much easier time as he beat Blaz Kavcic of Slovenia 6-1 6-1.
Czech Jan Hajek also made the second round after France's Edouard Roger-Vasselin retired during the opening set.
Ernests Gulbis of Latvia powered past Italy's Filippo Volandri 7-6(2) 4-6 6-3.
In Atlanta, crowd favourite James Blake put a disastrous first set behind him to get the better of sixth-seeded Ryan Harrison1-6 6-3 7-5 and move into the second round.
Blake, the one-time world number four, now plays Australia's Matthew Ebden, who beat Sergey Bubka Jr. of Ukraine 5-7 6-1 6-1.
Eighth seed Go Soeda also played out a three-setter, the Japanese edging Xavier Malisse of Belgium 4-6 7-5 6-4 to set up a clash with Igor Kunitsyn.
Ricardas Berankis, Ruben Bemelmans and Michael Russell were also winners against Dmitry Tursunov, Rajeev Ram and Alex Kuznetsov respectively.
Top seeds John Isner and Mardy Fish, who have received byes into the second round, are yet to enter the fray.