Verstappen flipped the script in FP2 after having trouble getting his RB19 car to ride smoothly over kerbs and bumps in FP1, which was led by Carlos Sainz of Ferrari.
Verstappen's position at the top of the times was assured when Sainz crashed out. The Dutchman's benchmark effort on soft tyres of 1m12.462s was 0.065s faster than Charles Leclerc's Ferrari.
The Spaniard ran into the wall at the swimming pool's entrance and, his steering broken, stumbled into the exit barriers.
Sainz still finished third despite a rough end to what had otherwise been a promising day, with Fernando Alonso 0.22 seconds behind Sainz in his Aston Martin, which for the first time this year features a package of updates.
Lewis Hamilton, who has won the Monaco Grand Prix three times, finished sixth in the Mercedes W14, another vehicle with notable upgrades.
With two red flags in FP1, Sainz wasn't the only driver to encounter the wall surrounding the perilous street track.