The Briton qualified behind Antonelli for both the sprint and the Grand Prix itself, but turned up the wick in both races to finish ahead of his teammate.
Russell was fortunate to claim third place in the 57-lap event, as he jumped Red Bull's Max Verstappen after the pitstop phase thanks to the lucky timing of a Virtual Safety Car period.
The 27-year-old has now claimed fourth podium of the 2025 season, and is the only driver to have ended every race in the top five.
Russell was delighted to celebrate on the podium once again, although he was subsequently admitted to the medical centre after feeling unwell during and after the race.
He admitted that he had issues with drivability of his W16 all weekend long.
He said: "I am really happy to come away with P3 today in Miami. I've been struggling a little more than usual this weekend and not felt as comfortable in the car as at previous races this season.
"I've been a little on the back foot but when it mattered, we've put in a good performance and come away with another strong result.
"Verstappen was close behind me after we pitted but I felt positive on the Medium tyre and knew I could manage my pace to keep him behind," added Russell.
The Mercedes driver congratulated McLaren on their domination of the Miami Grand Prix.
He continued: "Ultimately the McLarens had a decent advantage over the rest of the field so congratulations to them.
"It will be a tough ask to close them down, but we will keep working on doing that, and we're looking forward to the upcoming triple header in Europe, starting at Imola," Russell concluded.
Mercedes Team Principal Toto Wolff praised Russell for extracting the best possible result out of the weekend, given the dominance of McLaren.
He stated: "George drove a great race today and did everything he needed to do to claim third. It was another mature performance where he got everything out of the car that was there.
"Obviously, the gap to the McLarens was large though. That is disappointing but we are working hard to bring updates that will hopefully close that deficit.
"We've seen these performance gaps fluctuate over these first six races, and some weekends other teams get right in the mix at the front, but they are the team to beat right now."
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