Charles Leclerc finished third for Ferrari, after starting fourth, in the first race following a forced April break due to the Iran war leading to the cancellation of Middle Eastern rounds.
Mercedes pair Kimi Antonelli and George Russell crossed the line fourth and fifth respectively but the Italian was demoted to sixth after being given a five-second penalty for repeated track limits violations, with Russell moving up a place.
The drop meant the 19-year-old winner of the previous two grands prix in China and Japan saw his championship lead over Russell cut to seven points. It also meant Red Bull's four-times world champion Max Verstappen moved up to fifth, with Lewis Hamilton seventh for Ferrari.
Alpine's Pierre Gasly secured the final point in the 100-km race run in hot and humid conditions.
'Nice to be back on top'
Antonelli now has 75 points to Russell's 68 and Leclerc's 55. Norris, fifth overall, is on 33.
Norris took the chequered flag 3.7 seconds clear of Australian Piastri after starting from pole position and pulling away to lead untroubled in a car benefiting from a raft of upgrades.
"Nice to be back on the top step. A good day for us," he said of his first win since Brazil last November.
"I was pushing, trying to find that balance of pushing and staying relaxed to not make mistakes. A good start to the weekend but now I've got to do it all over again."
The main grand prix is on Sunday, when rain and possible lightning storms are threatened, with qualifying later on Saturday.
The win was a repeat of Norris's 2025 sprint success at the Hard Rock Stadium, where the Briton took his first career F1 win in 2024, and on Saturday he was presented with the winner's plaque by Reid Wiseman, commander of the recent Artemis II Lunar flyby mission.
The top three stood in a minute's silence for former racer Alex Zanardi, who died on Saturday at the age of 59. All the drivers and team bosses had also held a similar tribute on the grid before the start.
Antonelli made a poor start but recovered and had looked to get the better of Russell after a tussle for fourth place, the pair passing and re-passing early on, but the Italian proved too erratic.
"Kimi is so bad on wheel to wheel," Leclerc complained over the radio after they had battled for third, comments he later rowed back on as just the heat of the moment.
"We need to check what happened. The grip was very low, probably lower than we expected," Antonelli said of his start, where he dropped from second to fourth.
“After that, I was really frustrated and didn’t even drive well. I did a lot of mistakes and got track limits, which is something I need to avoid."
Mercedes boss Toto Wolff said the result also reflected Mercedes being out of sync with rivals who had brought major upgrade packages while the former champions have scheduled theirs for the next round in Montreal.
"It’s going to be a development race through the year and whoever brings a few tenths earlier will have the advantage," said the Austrian.
Racing Bulls' rookie Arvid Lindblad did not start due to a technical issue while Nico Hulkenberg was ruled out when his Audi caught fire on the way to the grid.