The powerful Querrey, who asked for a wild card into the tournament on Friday, had 13 aces during the 1-hour, 38-minute match.
Querrey took advantage of three of 10 break points and will face Christophe Rochus of Belgium next.
"He makes a lot of balls and he makes you work for every point," said Querrey, who reached the quarterfinals of San Jose and Memphis the past two weeks.
"I kind of had a little cold last week and early on in the first set I was feeling winded after some of those long points. He always makes you hit another ball on every point," he said.
"In general, I'm very happy because it was quite easy," said Koubek, who was sidelined for six months after surgery to repair a spinal disk last May. "It was a very solid match."
The 266th-ranked Koubek, who won the tournament in 2000, broke serve twice in the first set and once in the second set to secure the win.
"I only won three tournaments in my career so if I come back to one of those it's always something special," Koubek said. "It feels kind of strange because it was nine years ago.
"I must be an old guy on the tour," he said.
In other first-round play, fifth-seeded Steve Darcis of Belgium was upset by Guillermo Garcia-Lopez of Spain 6-3, 6-3 in the opening match of the day. Also, sixth-seeded Florent Serra of France beat Jarkko Nieminen of Finland 6-3, 7-6 (5).
Taylor Dent, also on the comeback trail following two back surgeries in 2007, joined fellow American Ryan Sweeting, Canada's Frank Dancevic and Russia's Evgeny Korolev in qualifying for main draw spots on Monday.
Dent, who thought he'd never play again and was out of action from February 2006 to May 2008, captured a 6-3, 6-3 win over Giovanni Lapentti of Ecuador to qualify.
Dent will play Mischa Zverev of Germany in the first round on Tuesday.