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.
Mother's Day 2018: Best deals, discounts, freebies to celebrate mom's special day
I don't love anyone like how I love my son! It also pays homage and highlights the several sacrifices they make on a daily basis. Anna Jarvis just wanted to honor her mother. "In the evening I may visit an old age home with a cake for abandoned mothers".
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.
Don't worry, Congress will come back: Siddaramaiah dismisses exit polls on Karnataka
A total of 2,654 candidates, including 216 women candidates were in the fray for the assembly elections this year. Mr Deve Gowda's party has said it is the Congress' "responsibility" to reach out if it did not get majority.
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.
OPEC chief: Ditching Iran deal would harm global economy
To pressure allies, the USA intends to apply "secondary sanctions" on non-American firms that do business with Iran. But that's exactly what Iran Oil Minister Bijan Namdar Zanganeh said on state television Thursday.
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