Russell was 0.106 seconds quicker than Ferrari's title leader Charles Leclerc, whose rival Max Verstappen suffered reliability problems for Red Bull.
Verstappen failed to set a time while team-mate Sergio Perez was third, ahead of Lewis Hamilton's Mercedes.
Fernando Alonso was fifth fastest for Alpine, from McLaren's Lando Norris.
Carlos Sainz crashed the second Ferrari midway through the session, his third key error in as many race weekends.
Sainz's accident caused a 10-minute stoppage in the session, and a second red flag when Nicholas Latifi's Williams stopped out on track meant the teams were unable to do any significant running in race trim in the final minutes.
Russell's performance came as Mercedes introduced their first significant upgrades of the season, which they started with a car that was close to a second off the pace.
And underlining the apparent step forward from the world champions, the Briton was second fastest behind Leclerc in the first session as drivers had their first taste of the new Miami street track at the Florida city's inaugural race.
It is too soon to draw any firm conclusions as to whether this is indicative of permanent progress for Mercedes or caused by a series of aspects particular to this weekend, but it was certainly the first sign that the team may be getting on top of the problems that have afflicted them this season.
The upgrade on the car is a lower-drag rear wing, as well as a revised front wing.
The team hoped that the rear wing would raise the speed at which the 'porpoising' problem that has hamstrung this season would instigate and it seems to have worked.
However, it could also be that circumstances have helped them.
The upgrade appears to have worked, but at the same time this is a lower-downforce track that might have helped their car's characteristics and the hot temperatures in Miami could have alleviated their problems with getting temperature into their tyres on a first flying lap - which has been a problem all season, but was not on Friday.
Russell said: "We don't really understand it to be honest, why we hit the ground running.
"We always knew the conditions here would suit us better. We have been struggling with tyre warm-up even in Bahrain when the track was really rough but this is the first real hot race of the season so for sure that's played a big factor. It's only Friday. Not getting too carried away.
"It has definitely been a really productive day for us and probably the most productive Friday we've had."
Hamilton had a less happy time. His car looked less stable out on track and he was slower than Russell all day, ending it 0.241 secs behind his team-mate.
"There is definitely positive elements from today. I'm still struggling with the car. George looked great but we are trying a lot of different things and we will converge and hopefully improve."
Behind Alonso and Norris, the top 10 was completed by Alpha Tauri's Pierre Gasly, Alfa Romeo's Zhou Guanyu, Alpine's Esteban Ocon and the Haas of Kevin Magnussen.
The second Alfa Romeo of Valtteri Bottas did not take part in the session after a crash in the first hour of running.
On the short race simulations that were completed at the end of the session, Perez appeared to have a slight advantage over Leclerc and then Russell.
Verstappen was late out for the start of the session after overheating in the first forced Red Bull to change his gearbox in the break.
And when he did go out on track, his car immediately suffered a hydraulic problem and he had to tour slowly around to the pits, during which time a rear brake disc also caught fire.
"This is an extremely painful day," Verstappen said. "Certainly here you want to get to know the track, but I only did four or five fast laps. We now have zero info on my car here."
-- Courtesy of BBC Sport