Spaniard Marquez, a Honda rider, completed the fastest lap over the 5.5km, 20-turn Circuit of the Americas at Austin, Texas, in 2mins 4.061secs with French Yamaha racer Johann Zarco second, .286 of a second back.
"Today went well enough and in the second session I started to feel more comfortable on the bike," Marquez said. "But there are some areas of the setup where we need to keep working hard, especially to improve the feeling with the front.
"The positive is that over the course of the day, we were able to complete a lot of work and try all the tires, even the soft one, to see how the bike reacts. In the afternoon we also took a step forward with the electronics, finding a good enough base, although we also want to sort out some more details there to improve the bike's behavior on the bumps."
Marquez, the reigning world champion, has won all four prior Moto GP events contested at the circuit from the pole.
Yamaha rider Vinales, who won the first two races at Qatar and Argentina, completed the fastest lap in the first run at 2:04.923 but was third on the day with a top time still .390 off his countryman's pace.
"It's my first time here with the Yamaha M1 and I felt great," said Vinales, who collected his first tour win in Texas at a 2014 Moto2 race.
"Of course we still have to work hard, especially in preparation for the last laps of the race, but I'm happy and confident. I'm sure that we can do a really good weekend."
Vinales was fourth at Texas last year riding for Suzuki.
Fourth on the day was Italy's Valentino Rossi, Vinales' Yamaha teamate, on 2:04.806.
Vinales leads the standings with 50 points to 36 for Rossi, who started third last year but crashed on the second lap.
"COTA is always a difficult track for us, but it's also very interesting," Rossi said.
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