The Briton came home 3.131 seconds clear of last year’s winner with championship leading McLaren team-mate Oscar Piastri taking third.
Four-time champion Max Verstappen of Red Bull came next ahead of seven-time champion Lewis Hamilton in the second Ferrari.
Norris became the first McLaren winner in Monaco since Hamilton, in his first title-winning season of 2008. It was his first Monaco triumph, his second this year and the sixth of his career.
French rookie Isack Hadjar finished sixth for the RB team ahead of Esteban Ocon of Haas, Liam Lawson in the second RB and the Williams pair Alex Albon and Carlos Sainz.
“Monaco baby, yeah baby!” screamed Norris from his car during his slowdown lap after closing to within three points of Piastri in the title race.
“It feels amazing. It’s a long and gruelling race. I was nervous into the last corner and we pushed, but we won in Monaco so it doesn’t matter how you do it.
The race began on a clear, dry and sunlit afternoon with the teams choosing a wide range of tyres ahead of the first mandatory two-stop race.
Norris made a solid start from pole, but went close to sliding off at Ste Devote. He held on to resist Leclerc before a quartet of tail-enders – including Yuki Tsunoda and Pierre Gasly made early stops.
A skirmish involving Kimi Antonelli and Gabriel Bortoleto was followed by early use of a virtual safety car (VSC) which prompted the first stops, but most stayed out with Norris hanging on in front.
Yellow flags waved again on lap eight when Gasly lost control of his Alpine at the Nouvelle Chicane and ran into Tsunoda’s Red Bull, damaging his front left wheel. He limped back to the pits and retired.
The disrupted order was affected by off-set strategies as teams sought to control one car’s pace to create space for a pit-stop for the other.
This ploy required Hamilton, Lawson and Sainz, among others, to sacrifice their races, in the process slowing the field and creating traffic jams.
Hamilton pitted on lap 18 and Norris on 20, the race leader resuming in fourth as Hadjar, making the most of RB’s tactics, pitted for a second time and returned in eighth.
By lap 30, despite the pit-lane chaos, it was ‘as you were’ at the front with Norris leading Leclerc, Piastri and Verstappen – and Hamilton fifth, despite his three-place penalty.
Obeying team orders, Hamilton built a deficit of 14 seconds behind Verstappen, to create a gap for Leclerc’s second stop before Alonso retired at the Rascasse.
After more pit stops and with 25 laps to go, Verstappen led Norris from Leclerc and Piastri fourth, but the champion had a stop to make as attention switched to incidents that saw George Russell and Antonelli cut the chicane to pass a deliberately slow Alex Albon.
Russell refused to hand back the place and was given a drive-through penalty. “I prefer not to speak,” he said, clearly furious.
For Mercedes, it was a day to forget.
“It’s not way we want to race,” admitted Williams’ chief James Vowles, having schemed his men to ninth and 10th.
Verstappen hung on in front on his old tyres, hoping for a red flag stoppage to gift him a cheap stop as he backed off and compressed the front group into the closing laps.
He knew, too, that he faced a 30-second penalty if he did not stop again and would finish fourth anyway before he came in ahead of the final lap to rejoin behind the top trio. (AFP)