Verstappen got the better launch from second on the grid to run side by side with pole-getter Leclerc as they hit the brakes for the first turn, but the super low grip surface off the racing line sent the Dutchman sailing off the track, with Leclerc helpless but to follow him from the outside.
They joined just ahead of the pack but with Verstappen having taken the lead - unfairly, the stewards judged, and he was soon slapped with a five-second penalty for passing off the track.
But Verstappen had a more pressing problem to deal with. In the chilly night-time conditions he had overworked his tyres and suddenly felt the grip expiring. He had built a 2.5-second lead, but Leclerc sliced that down to almost nothing on lap 16.
The Monegasque made an easy pass down the Las Vegas Strip, out-braking his rival into he chicane to take the lead.
Verstappen’s afternoon was going from bad to worse. He was hauled into the pits for a new set of tyres and to serve his penalty, dropping down to 11th. He then tripped over George Russell in a fight at the right Turn 12 left-hander - the Briton hadn’t seen him coming hard on the brakes from a long way back and turned in, leaving both with damage.
But in an ironic twist, the damage strewn over the circuit triggered a safety car, gifting Verstappen a cheap second pit stop and a ticket back into the grand prix.
It was also a boon for teammate Sergio Pérez, who was on a recovery of his own.
The Mexican had been caught up in a first-corner tangle caused by Fernando Alonso, forcing him into an early first stop for repairs.
An early safety car - for a big crash for Lando Norris, whose McLaren snapped from under him at the high-speed turns 11 and 12 and crunched up against the barriers - allowed him to rejoin at the back of the pack, from where he exercised excellent pace to rise up the order.
The second safety car then turned what would have likely been a hefty haul of points into a shot at victory by gifting him a cheap second stop.
At the restart the net podium order read Leclerc from Pérez and Verstappen, but the leader was on older tyres. Ferrari had opted for track position over fresh rubber in the hope the SF-23’s straight-line speed would be enough to make the difference.
Pérez tried to punish him from the strategy, almost immediately blasting past at the end of the Strip once DRS was enabled, but the Monegasque bit back three laps later with an identical move to resume top spot.
But the short squabble dropped both into Verstappen’s clutches. The Dutchman needed just two clinical passes on laps 36 and 37 to snatch the lead, from where he massaged open a gap that would secure him victory.
The fight for second wasn’t yet finished. Leclerc’s older tyres were wearing, and on lap 43 of 50 he made a mistake under braking at turn 12, opening the door wide to an easy pass that seemed sure to secure second for Pérez.
Leclerc seemed dispirited, but he bided his time until the final lap for a Hail Mary pass into the big-braking turn 14.
Pérez was caught napping, and the pair ran almost side by side exiting the chicane towards the chequered flag.
In a photo finish Leclerc snatched the place, the margin just 0.2 seconds.
Despite the disappointment, it was enough for Pérez to secure second in the championship, Red Bull Racing’s first one-two finish in the drivers title standings.
George Russell took the flag fourth but was demoted to eighth with his penalty for colliding with Verstappen.
Esteban Ocon was the beneficiary, capping off a 12-place recovery thanks in equal parts to a big start and excellent execution of a one-stop race.
He had to defend hard on older tyres from Lance Stroll, who rose a sensational 14 places from his starting position, beating the Canadian by 1.4 seconds with Carlos Sainz and Lewis Hamilton in tow.
Fernando Alonso finished ninth ahead of Oscar Piastri, for whom contact with Hamilton on lap 16 forced him into an unscheduled pit stop that undermined a strong race, leaving him battling for a final point and a consolation score for fastest lap.