A collision between Logan Sargeant and Kevin Magnussen brought out a safety car, with McLaren capitlising on it by pitting Norris, where he emerged ahead of Max Verstappen.
Norris not only held off Verstappen for the final part of the race, but managed to create a 7.6 second gap to the Dutch driver by the end.
Can Norris compete for a world title?
McLaren have made significant improvements since the Miami GP last year, where Norris finished just 17th.
Following development changes, McLaren have emerged ahead of Mercedes as one of the top teams on the grid.
The team also brought new upgrades to Norris’ car in Miami including a new front wing and a sidepod inlet.
Speaking after the race, team principal Andrea Stella seemed surprised that the upgrades had enhanced the speed of the car compared to Red Bull.
“We knew that the car was quick, [although] it's a bit of a surprise. But we take it positively and we take it for the future as well,” he said.
Whilst a world title bid is an unlikely prospect for the team this year, Norris’ performance bodes well for the future.
Speaking after the race Sky Sports pundit Danica Patrick appeared confident that Norris will win a championship.