Hamilton will be trying to win his second race in a row and add to his four-point lead over Vettel in the drivers' standings.
On the second run, Hamilton reduced his time to a 1m16.173s.
But Hamilton still expects his title rival to be challenging for pole position in today's qualifying shoot out.
Hamilton had also won in Azerbaijan two weeks ago, but that victory came mostly because of incidents involving his closest competitors, including a blown tire for Bottas and a crash between Red Bull teammates Daniel Ricciardo and Verstappen. A Virtual Safety Car period to recover Esteban Ocon's stricken Force India saw Vettel pit for a new set of medium tires - as all of the front-runners were using after starting on softs - but dropped him to fourth place on the road.
Apart from Australia, where Hamilton sped away from pole, Vettel has nailed every qualifying session.
The very clever tactic Vasyl Lomachenko used to beat Jorge Linares
The right hand is working and landing regularly, and it could be an early night for Barrera if he doesn't defend against it. Ukrainian Vasyl Lomachenko had the first lightweight fight with Jorge Linares from Venezuela in NY .
A last gasp run on the harder compound tyres brought Vettel and Raikkonen to the Mercedes drivers but unable leap-frog them.
Ricciardo, whose Red Bull featured notable aerodynamic upgrades for the opening round of the European season, was only one-tenth of a session adrift of Hamilton.
Lewis Hamilton responded by saying that he doubted the changes will make the racing experience any good, that too at the cost of slower cars. Verstappen also went off the track, as did Raikkonen shortly before enduring the mechanical problem.
The Finn plays second fiddle to his teammate throughout the season and may be tempted by top-billing elsewhere, while Mercedes themselves may decide they can get a better deal with a new driver.
Magnussen qualified seventh. Grosjean was 10th in Q3, despite only being 0.2s adrift of his team-mate's time.
Uber unveils flying taxi prototype at Elevate summit
Tuesday's Uber Elevate Summit has unveiled the rideshare company's latest plans to venture into the untapped world of air taxis. As part of its second annual Elevate Summit , Uber announced that it has entered a partnership with E-One Moli Energy (Moli).
New Zealander Brendon Hartley of Toro Rosso was not among the runners following his huge accident at the end of final practice, which left the rear end of his vehicle wrecked after spinning into the barriers at high speed.
Miami and Formula 1 are working to bring an race to the city in 2019 and a track layout has even been released. Despite finishing free practice one only 19th fastest, he expressed satisfaction with the session. Generally he likes spinning, but on the first lap is not a good time to do it with everyone there.
Those who feel that the current driver line up of Lance Stroll and Sergey Sirotkin is the worst in the team's history, could have their case strengthened this weekend.
Stroll almost hit the tire barriers after going off the track with about a half-hour left in the first session.
Brad Stevens 'Non-Committal' on Celtics' Starting Lineup vs. LeBron James, Cavs
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