Verstappen will start ahead of Fernando Alonso (Aston Martin) and Charles Leclerc (Ferrari) after the one-hour qualifying session, which is split into three segments with five cars each being knocked out in Q1 and Q2 before the top-10 shootout of Q3.
Besides the thrilling ending to Q3, where pole changed hands four times in the final two minutes, the big shock was last year's race winner Sergio Perez crashing out of Q1 inside the first five minutes of qualifying in his Red Bull.
Verstappen set the early pace at 1m13.784s, 0.066s clear of Perez's 1m13.850s. Perez then crashed heavily on his second push lap at Sainte Devote, after losing control of the rear of his car, and slammed the barrier to cause a red flag.
Verstappen reset the P1 bar at 1m13.038s at the resumption, before Alonso raised it with 1m12.886s. Verstappen responded with 1m12.644s, before Yuki Tsunoda (AlphaTauri) grabbed the top spot by 0.002s with 1m12.642s. Verstappen wasn't to be denied, however, setting 1m12.386s on his final lap.
Falling at the first hurdle were Logan Sargeant (Williams), the Haas duo of Kevin Magnussen and Nico Hulkenberg, Zhou Guanyu (who had topped the session briefly for Alfa Romeo before Perez shunted) and the gutted Perez.
Verstappen set the initial pace at 1m12.038s, 0.069s ahead of Alonso. Verstappen then lowered the P1 time to 1m11.908s, 0.195s quicker than Leclerc.
In the closing moments, Norris slammed the barrier at Tabac after he'd already clipped the wall on the exit of the Nouvelle Chicane, but just squeaked through to Q3 by 0.018s.
Knocked out at this point were Norris's McLaren team-mate Oscar Piastri, Nyck de Vries (AlphaTauri), Alex Albon (Williams), Lance Stroll (Aston Martin) and the Alfa of Valtteri Bottas.
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On the first runs, Verstappen only lapped in 1m12.102s before Alonso took provisional pole with 1m11.706s after "pushing like an animal", ahead of Ferraris of Carlos Sainz (by 0.029s) and Leclerc (by 0.053s).
Verstappen pushed again on the same tyres, producing 1m11.654s to take back pole following a stellar final sector, while Lewis Hamilton jumped to third doing likewise in his Mercedes.
On the final runs, Esteban Ocon then grabbed P1 for Alpine with 1m11.553s, a tenth faster than Verstappen.
Leclerc wrested that away on 1m11.471s, before Alonso grabbed P1 with 1m11.449s - faster by 0.022s. But Verstappen wouldn't be denied, though, unleashing 1m11.365s on his final lap.
Alonso - who was just 0.084s slower - will start second, ahead of Leclerc, Ocon, Sainz, Hamilton, Pierre Gasly (Alpine), George Russell (Mercedes), Tsunoda and Norris.