Ferrari's Charles Leclerc overtook Red Bull's Sergio Perez on the last lap to grab second place ahead of the Mexican with French driver Esteban Ocon of Alpine finishing fourth at the end of a race which saw multiple lead changes and plenty of overtaking.
Verstappen had been highly critical of the return of Formula One to Vegas after a 41-year absence, saying the event was "99 percent show", but as he drove past the finish line he celebrated with a chorus of 'Viva Las Vegas' on the team radio.
"He loves a race like that. Even though he was on the end of a penalty. When he came back...the way he fought. I think he changed his mind about Vegas," said Red Bull team principal Christian Horner.
The show was certainly evident with pre-race grid packed with a host of celebrities from the world of music, sport and entertainment as memories of the embarrassment of the opening practice session on Thursday being stopped early due to a loose water valve on the track, faded.
When the race was under way, the low grip on the track made sure there was no shortage of incident, overtaking and lead changes, as the night race delivered the entertainment the American promotors had craved from the new event.
The Dutchman won by 2.070 over Leclerc but had to work for his victory in what was the latest starting race in F1 history
"It was a tough one. I tried to go for it at the start. We both braked quite late and I just ran out of grip, so we ended up a bit wide," said the triple world champion.
'A lot of fun'
"The stewards gave me a penalty for that and it put us on the backfoot. I had to pass quite a few cars and there was the Safety Car, so at that point there was a lot going on," added Verstappen, summing up the race as "a lot of fun."
The Dutchman, starting second on the grid, grabbed the lead in the first turn of the opening lap but was penalised five seconds for pushing Leclerc wide.
The tricky surface was evident when McLaren's Lando Norris crashed out, spinning into the barrier on turn 14 of the fourth lap. The British driver was taken to hospital for precautionary tests.
Ferrari's Monegasque driver Leclerc kept in close touch though and was able to get the lead back, overtaking Verstappen on lap 16.
The Dutchman had to serve his penalty in the pit, leaving him plenty of work to do to regain his lead and when Leclerc went into the pits on lap 22, Perez took over at the front.
Mercedes' George Russell made contact with Verstappen, clipping his front wing, an incident which resulted in a five second penalty for the British driver who crossed the line fourth but ended in eighth place.
Leclerc and Perez jousted for the lead but Verstappen was ominously gaining ground and after he passed Perez he then made his decisive move on lap 37.
From then on, Verstappen never looked back, Leclerc slipping into third spot after he out-braked himself and allowed Perez to fly by.
But there was one more twist in the tale as Leclerc brilliantly moved past Perez to grab second place.
"What a race. I enjoyed it so much. I'm of course disappointed to only finish second, but that's the best we could do," said Leclerc.
"And we needed it. The weekend didn't start the way we wanted it to start but I am so happy it ended that way. It's such an incredible sport. The energy around the city is incredible and I at least really enjoyed today," he said.
Ferrari's Carlos Sainz, who had started in 12th place after being sanctioned with a harsh ten-place grid penalty, rose to finish sixth behind Aston Martin's Lance Stroll.
The Mercedes pair of Lewis Hamilton and Russell finished seventh and eighth with Aston Martin's veteran Spaniard Fernando Alonso ninth and McLaren's Australian Oscar Piastri tenth.
