The 26-year-old Monegasque driver clocked a best lap in one minute and 11.369 seconds to outpace Red Bull's Verstappen by 0.197 seconds.
Lewis Hamilton maintained his Friday pace for Mercedes to finish third ahead of Oscar Piastri of McLaren, Sergio Perez in the second Red Bull and George Russell in the second Mercedes.
Carlos Sainz was seventh for Ferrari ahead of Lando Norris in the second McLaren, Yuki Tsunoda of RB and Fernando Alonso of Aston Martin, once again shining on the roads of the famous Mediterranean street track.
Leclerc drove with impeccable precision and speed, but it was the attacking verve of Verstappen, in his uncomfortable Red Bull, that caught the eye as he charged hard in the final frantic minutes.
"If I do more laps like this I'll end up in the fence," said the Dutchman in exasperation, punctuated by expletives.
He was then called to see the stewards for driving too slowly in the final sector.
On a warm sunlit Riviera morning, Russell was the first out of the pit lane on fresh soft tyres, immediately reporting that his steering was distinctly different to Friday when he complained of lack of precision.
"There's no vibrations, which is obviously good," explained the Mercedes driver.
Kevin Magnussen set a first marker time for Haas before Hamilton went top before his former team-mate Valtteri Bottas lost control of his Sauber and smacked the barriers as he came out of the Swimming Pool complex.
Red flag
This prompted a red flag as he was stranded at the Rascasse hairpin until he was recovered. On resumption, Leclerc clocked 1:12.521 to move clear of Piastri by 0.163 seconds, a time he trimmed down to 1:12.092.
Behind him, Verstappen was showing improved form after Friday when his Red Bull was jumping excessively and was soon up to third and then second.
"I know where we can gain time," the reigning world champion reported. "It's just not possible. We know why."
As he struggled, Sainz jumped to second, two-tenths adrift of team-mate Leclerc before Hamilton narrowly avoided the barriers, sliding over the kerbs at the Swimming Pool.
Leclerc then clocked 1:11.977 to go three-tenths clear while Hamilton and Russell returned to the pits for new tyres, Mercedes clearly sensing potential for strong grid positions in qualifying later Saturday.
Stimulated by the contest, a seemingly-inspired Leclerc did a lap in 1:11.369 to go six-tenths clear of Sainz with Alonso third, the Ferrari duo clearly relishing their car's Monaco set-up.
With 11 minutes remaining, Hamilton improved again to jump above Alonso for third, six-tenths off Leclerc who was close to his Friday best, which was faster than last year's pole lap by Verstappen.
It signalled a final flurry from all of the leading contenders as Vertstappen, twice, and Piastri, jumped to second in a very competitive finale that promises a close battle for grid spots later Saturday.
