Reigning world champion Verstappen pipped Red Bull teammate Sergio Perez by just 0.073s to top a crucial final hour of practice ahead of what is arguably the most important qualifying of the season.
But a true picture of the competitive picture was skewed after the closing stages of FP3 were interrupted by several stoppages that prevented drivers from improving.
Hamilton had just set the fastest first sector of anyone before he slid into the barriers at Mirabeau, causing damage to his newly-revised W14 and bringing the session to an early end.
That came shortly after Kevin Magnussen caused a pair of yellow flags when he first ran down the Sainte Devote escape road, before grinding to a halt in his Haas at Portier.
The Magnussen and Hamilton incidents curtailed the final qualifying simulation runs of practice.
Lance Stroll was third-quickest and 0.166s off the pace, while Aston Martin teammate Fernando Alonso was left down in 14th after the Spaniard was one of the drivers to have his soft tyre runs ruined by the late drama.
Alonso, who has been widely tipped as a potential contender for pole position this weekend, had gone purple through the first sector before Magnussen stopped on track.
Carlos Sainz was fourth in his Ferrari, ahead of McLaren’s Lando Norris and Alpine’s Pierre Gasly.
Charles Leclerc was seventh, with Hamilton, Esteban Ocon and Valtteri Bottas rounding out the top 10 for Ferrari, Mercedes, Alpine and Alfa Romeo respectively.