Thanks to Daniel Ricciardo’s exclusion from qualifying Norris was promoted to ninth on the grid behind McLaren teammate Carlos Sainz and Renault’s Nico Hulkenberg.
But an incident between those two opened up the chance for the Brit to move up into seventh which he occupied for the majority of the race other than dropping down to P13 after his pitstop.
The 19-year old finished three seconds behind Red Bull’s Alex Albon after holding off Toro Rosso’s Pierre Gasly towards the end of the race once the safety car periods had finished.
“I don’t think we could have done better than seventh,” Norris said after the race.
“It was a shame about Carlos getting hit by Hulkenberg at the beginning, because I think we could both have been in the points today.
“At the same time, from my side, it was a tough race, especially the final 10, 15 laps, I was under quite a bit of pressure...
“I was having to push, which was fun, because for the rest of the race we were just driving around so slowly.”
McLaren edged further ahead of rivals Renault in the constructors championship, leading them by 22 points because of Norris’ seventh place in his debut at Singapore.
“I mean, I’m tired,” Norris added when asked how he was feeling.
“But because the first 30 laps were so under the limit, literally just driving around trying to not to wheelspin or lock up or understeer, it was fairly relaxed.
“It was more like a 20-lap race.”