The Monegasque driver was fast throughout the day as he clocked a best lap in one minute and 11.278 seconds to finish 0.188 seconds clear of Hamilton, who was fastest in the opening session earlier in the day.
Fernando Alonso was third for Aston Martin, like Hamilton showing his experience with a rejuvenated performance around the merciless barrier-lined Mediterranean street circuit.
Championship leader Verstappen was only fourth, half a second adrift of Leclerc, who has yet to claim a podium finish on the roads he knows so well, proving his fears that Red Bull might struggle.
"I'm jumping like a kangaroo and getting headaches," complained the Dutchman.
Lando Norris, winner of his maiden F1 race in Miami three weeks ago, was fifth for McLaren ahead of Carlos Sainz in the second Ferrari, Lance Stroll in the second Aston Martin and Sergio Perez in the other Red Bull.
A lively Alex Albon was ninth for the improving Williams team and George Russell 10th in the second Mercedes, ending the session complaining of steering problems.
Rain had threatened ahead of the second session which began with Hamilton again leading the exit from the pit lane followed by Kevin Magnussen and Russell, all three showing some urgency in reaction to the principality's capricious micro-climate.
Perez, Magnussen, Hamilton and then Verstappen set the pace before Hamilton took control only for Verstappen, in 1:13.265 and then Leclerc, in 1:12.372, regained the initiative.
In a busy opening charge, Logan Sargeant kissed the barriers in his Williams.
"Oh, I've hit the wall!" he exclaimed, but without causing serious damage before most came in for a set of soft tyres to do some qualifying simulation laps before the expected rain.
Leclerc continued to shine and trimmed his best to 1:11.278, clear of reigning world champion Verstappen, whose Red Bull team-mate Perez was struggling.
"The ride is horrendous," he reported. "I can't see the apex of Turn Three. It's so violent."
Showing his individual brilliance, Alonso then went second before Verstappen hit the barriers at Portier, followed by Yuki Tsunoda.
The Spaniard was clearly in the mood and relishing his Aston Martin's upgrades.
As they all pushed for speed, Esteban Ocon joined the list of barrier-bashers. "I've hit the wall," he cried, but continued.
Like the rest, Alpine faced a long evening checking and repairing damage.
Shortly before most teams switched back to harder compounds for the final minutes, Hamilton went second, just a tenth off Leclerc's pace, a lap that confirmed the seven-time world champion had refound his mojo on one of his favourite tracks.