The McLaren driver finished behind race winner Kimi Antonelli and runner-up Lando Norris.
That was thanks in part to pitting late and maximising his tyre life to execute a pass on Ferrari’s Charles Leclerc with a little more than a lap left in the race.
When Leclerc spun coming out of Turn 3 on the final lap, that all but guaranteed Piastri’s podium finish.
“Our starts as a team have always been strong, and I think today was another good one,” said Piastri.
“And then after that, the pace was strong. The first stint before the Safety Car, I made a few mistakes and just wasn’t as good as I hoped it would be.
“But I think the second half of the race felt much more comfortable.
Secure your spot today.
“I think the pace was just a lot better as well and was able to chase down George (Russell) and obviously Charles (Leclerc) at the end as well. So very happy about that.
“In terms of the result, very happy,” he added.
“Obviously, for a long part of that race, it definitely wasn’t looking like a podium, so to end up in third is a really good result.
“The team has done a great job with the upgrades this weekend. I think we did a great job as well in hitting the ground running on Friday and then maximising things.”
Leclerc throws Miami podium ‘in the bin’ with brain explosion
It was a somewhat turbulent weekend for Piastri, who qualified third for the Sprint before going on to finish second behind Norris.
Piastri then qualified seventh for the Grand Prix, a result he labelled “random” and somewhat perplexing.
“Qualifying was a little bit harder to read,” said Piastri.
“I think our impression after qualifying was that the others had just kind of maximised what they had a lot more, but we knew we had a little bit to find again after qualifying.
“But I think the pace we had today as a team was really strong, so that was really encouraging.
“Obviously, for myself, I think the whole weekend I’ve been just that tenth or two off most of the time, which has made life a little bit trickier than it should have been at points.
“In terms of being able to maximise the result after qualifying, I think I did a good job today.”
McLaren and Mercedes foreshadowed upgrades for Miami and the subsequent Canadian Grand Prix.
Piastri said he is interested to see how he and Norris stack up against Antonelli and George Russell in Montreal.
“As Lando said, we kind of need to see where we stack up at a few different tracks,” said Piastri.
“I think especially in the Sprint side of this weekend, to have a one-two in the Sprint on pure pace, that was a pretty big surprise for us. So, things are working well.
“We expected the upgrades to be a good step forward and they have been, and hopefully they are again in Canada.
“But obviously Mercedes didn’t bring a lot this weekend and they also have an upgrade package for Canada, so we’ll have to wait and see how much that’s worth for them.”
Piastri sits sixth in the world championship with 43 points to his name, 57 points in arrears of leader Antonelli.
Formula 1 returns on May 23-25 for the Canadian Grand Prix.
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