Polesitter Leclerc defied expectation by running a two-stop strategy but his late push on fresh tires failed to produce enough pace to reel in the champion as Verstappen rose from seventh.
Leclerc had his hopes bolstered by a late safety car that had the potential to throw a spanner in the works, but it was slow to pick up the leaders and duly denied a thrilling sprint to the finish and scuppered any Ferrari comeback.
That allowed the Red Bull driver to claim his 31st top-flight victory, fifth in a row and 11th of the season to close to within two triumphs of the record for the most successful F1 season.
After a change of internal combustion engine on the advice of supplier Honda, Verstappen lined up seventh thanks to a five-place grid penalty following his lap for second in qualifying.
His RB18 was shod in the softest available C4 tire to launch well and claim fifth swiftly following an anti-stall trigger for third-starting Lando Norris and a pass on Fernando Alonso.
Verstappen kept climbing in the early stages of the 53-lap 100th anniversary race at Monza. He relegated AlphaTauri pilot Pierre Gasly for fourth at the end of lap one before diving past 2021 Italian GP winner Daniel Ricciardo under braking into the first chicane for a provisional podium.
That left only Leclerc and second-starting George Russell up ahead, the Mercedes holding firm after aborting the first chicane while squabbling with the Ferrari for the early lead.
Despite the W13 separating the pair, Leclerc and Verstappen traded early fastest lapse over the timing line as a net 2.5s split the protagonists.
Then the Red Bull claimed second with a great run out of Ascari before combining DRS and the tow to pass Russell cleanly down the main straight to tee up the fight for the win.
With Verstappen a couple of tenths faster per lap, Ferrari attempted to twist by using a virtual safety car – called when Sebastian Vettel parked up with a smoky engine – to give Leclerc a cheaper pitstop.
He stopped for a set of mediums on lap 13 with a swift 2.2s service just as the green flags were waved to dent the effectiveness of the undercut and Leclerc was released in third with 18s to find.
Despite his aging softs, Verstappen was able to hold a decent pace – lapping only 0.5s slower than Leclerc while holding a 10.2s cushion to Russell as Leclerc trailed by a further 4.1s.
As the F1-75 began to make gains, Verstappen pitted for mediums on lap 26 and courtesy of a quick 2.4s stop, came out only a touch over 10s adrift of the leader.
Verstappen’s fresh rubber enabled him to close the gap to 5.4s when Ferrari called Leclerc in again on lap 34 for softs seemingly for a straightforward run to flag, the Red Bull returning in second over Russell.
Leclerc’s initial pace was subdued but he managed to turn up the wick to lap 0.4s faster than Verstappen as the gap stood at 18s with 10 laps to go.
But a spanner was thrown in the works on lap 47 when Ricciardo parked up out of Ascari with an engine failure to trigger a safety car, which was deployed late but Verstappen pitted next time around for new softs and Leclerc swapped to used C4s along with Russell in third.
With the field well spread out, the safety car picking up Russell instead and then the lapped cars of Valtteri Bottas and Yuki Tsunoda splitting the lead duo, plus the McLaren taking time to be cleared by the crane, the race was not restarted to deny a sprint to the flag.
As such, Verstappen secured the win over Leclerc as Russell completed the podium, while Carlos Sainz turned in a rapid first-stint ascension to offset his back of the grid penalty and snare fourth.
Lewis Hamilton did similar, notably holding onto his spikey Mercedes while chasing Alonso plus performing a slick double pass on Norris and Gasly to bag seventh place.
Sergio Perez was able to make the flag despite a persistent brake fire at his first stop for hard tyres, as Norris claimed seventh over Gasly.
Formula E champion Nyck de Vries equaled Williams’ best result of the season in ninth to cap off his fine substitute appearance for an appendicitis-side-lined Alex Albon.
Zhou Guanyu, meanwhile, completed the top 10 for Alfa Romeo ahead of Esteban Ocon and Mick Schumacher.
Behind Bottas and Tsunoda, Nicholas Latifi and Kevin Magnussen (picking up a 5s penalty for aborting the first chicane) completed the runners.
Alongside Ricciardo and Vettel, Lance Stroll and Alonso (suspected water pump failure) were forced to pull up early.