The McLaren driver took the lead from poleman Charles Leclerc off the road and managed the primary half of the race.
However he was eventually passed by race winner Max Verstappen on lap 28, earlier than Lewis Hamilton additionally made it by to take second place for Mercedes.
It marked Norris’s fourth consecutive grand prix podium, repeating his third-place end final trip in Qatar.
Norris blamed the excessive degradation and temperatures for his struggles: “Sure, simply main the race. I might management it quite a bit, however simply not sufficient as we speak. However I am joyful. It was a very good race for my aspect.
“We knew our struggles, we knew what was going to be tough as we speak. And it was simply the degradation however the tempo over the primary 10 laps of each stint, the tempo to start with was robust.
“I simply could not maintain on lengthy sufficient. So we’re getting there. Progress, progress each weekend. Just a few extra steps wanted.”
Picture by: Sam Bloxham / Motorsport Images
Lando Norris, McLaren MCL60, Max Verstappen, Purple Bull Racing RB19
The McLaren driver put up an aggressive defence towards Hamilton, who finally used DRS to nip previous on the exit of Flip 1.
Carlos Sainz had appeared set to shut on Norris within the closing phases, however the Ferrari driver finally completed 4.4s adrift.
Norris added: “I needed to attempt, proper? However I simply could not do it. I did not have sufficient tyres left on the finish, you noticed how rapidly he pulled away on the finish. So you understand, I at all times needed to take care of my very own race.
“I did the perfect I might. I needed to push and take care of the tyres, and it was simply too tough as we speak. So possibly if it was a cooler monitor it will have suited us a bit of bit extra nevertheless it wasn’t. However I am nonetheless joyful.
“The group have completed a wonderful job to complete on the rostrum right here. It was higher than we have been anticipating coming into the weekend. So very joyful.”