Sauber driver Gutierrez had impressed in Austin qualifying as he took 10th place, but he was adjudged to have impeded Pastor Maldonado, earning him a 10-place penalty.
Button knew from Friday that he faced a three-place drop, having overtaken when the red flags were out during the complicated opening practice session. The McLaren man struggled for pace in qualifying anyway, and was only 13th quickest.
Pic's five-place penalty was awarded after Caterham had to break the gearbox seals on his car to fix an issue. He had been 21st in qualifying.
Max Chilton, who qualified last for Marussia, was also found guilty of blocking in qualifying, with Maldonado and Adrian Sutil on the receiving end. As he could not receive a grid demotion, he will have to take a drive-through penalty within the first five laps of Sunday's race.
At the front, Sebastian Vettel beat Red Bull team-mate Mark Webber to pole position after a close battle, with Romain Grosjean and Nico Hulkenberg earning the row two spots.
1. Sebastian Vettel Red Bull-Renault 2. Mark Webber Red Bull-Renault 3. Romain Grosjean Lotus-Renault 4. Nico Hulkenberg Sauber-Ferrari 5. Lewis Hamilton Mercedes 6. Fernando Alonso Ferrari 7. Sergio Perez McLaren-Mercedes 8. Heikki Kovalainen Lotus-Renault 9. Valtteri Bottas Williams-Renault 10. Daniel Ricciardo Toro Rosso-Ferrari 11. Paul di Resta Force India-Mercedes 12. Nico Rosberg Mercedes 13. Felipe Massa Ferrari 14. Jean-Eric Vergne Toro Rosso-Ferrari 15. Jenson Button McLaren-Mercedes 16. Adrian Sutil Force India-Mercedes 17. Pastor Maldonado Williams-Renault 18. Giedo van der Garde Caterham-Renault 19. Jules Bianchi Marussia-Cosworth 20. Esteban Gutierrez Sauber-Ferrari 21. Max Chilton Marussia-Cosworth 22. Charles Pic Caterham-Renault
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