Indeed it was Red Bull's Daniel Ricciardo who split the Mercedes duo with Hamilton, who wrapped up his third title here a year ago, only third fastest, two tenths of a second adrift of Rosberg.
Were Rosberg to deny Hamilton a fourth world title this year, then it would represent the first time the German has outscored him in their four seasons together at Mercedes.
Verstappen and Ricciardo are the only winners apart from the Mercedes pairing this season and have been getting closer to the dominant duo in recent weeks.
Hamilton has been a Texas favorite with his three wins in four years and he returned this year facing a 33-point deficit behind Rosberg in the title chase. Equally, they can help Rosberg by making life hard for the Briton.
Daniel Ricciardo went out on softs in the Red Bull, and went nearly a tenth of a second quicker than Rosberg.
Nico Rosberg has a commanding lead over Lewis Hamilton in the driver's championship.
But, after beating his Mercedes team-mate Rosberg to pole by two tenths of a second, a smiling Hamilton refused to entertain the idea that his return to form could yet prove fruitless.
The fifth United States Grand Prix at the Circuit of the Americas will start at 3 PM Eastern time tomorrow.
It was therefore amusing to see Hamilton summoned before the same journalists for the FIA Press Conference again in Austin, a second consecutive event which is somewhat unusual.
As promised, Lewis Hamilton had his phone ready for a picture. Rosberg admits he struggles with the turn, where Hamilton got the inside line at the start in 2015 and bumped him wide.
"It just came about, and I've been feeling good with it, and I'm sticking to it", he said. And if Rosberg wins Sunday, it puts him within range of the single-season record of 13 victories shared by Schumacher (2004) and Vettel (2013).
"When they bought Lotus, it was not the easiest situation, so it will take time to rebuild, but what I see is a good future and a massive challenge, but I am very up for that and want to build a success story with them".
Renault-bound Nico Hulkenberg was seventh for Force India ahead of Valtteri Bottas and his Williams team-mate Felipe Massa and Carlos Sainz of Toro Rosso.
Meanwhile, the four-times world champion Sebastian Vettel has clearly not given up on Hamilton winning a fourth title this year.
Hamilton had just jetted in from becoming the first Formula One driver ever to be a guest on The Ellen DeGeneres Show.