Verstappen and Ocon were part of a gaggle of drivers that backed up at the end of the main straight as they prepared to start their final laps of the session.
Keen to get a clear lap and worried about complying with the FIA's minimum delta requirements, Ocon passed Yuki Tsunoda, Zhou Guanyu and his own team-mate Pierre Gasly before blasting by Verstappen just before the start of the lap.
A clearly irked Verstappen said, "What the f*** is that Alpine doing?" and then repaid the compliment by diving down the inside at the first corner, forcing Ocon wide before the Frenchman nipped back past as the Red Bull driver abandoned his lap.
The incident ruined Ocon's first sector and left him in 17th at the end of the session, while Gasly demonstrated the potential of the A523 by going on to qualify fifth.
Informed that he had failed to make the cut, Ocon told his team: "That's a joke honestly, Verstappen diving into one like crazy."
Ocon and Verstappen famously have some history, having raced each other in F3 in 2014 and tangled in the 2018 Brazilian GP.
Pressed on the Verstappen incident, Ocon insisted that he was trying to stick to the FIA's minimum delta rules.
"The difference between me and him is that I have to do that lap because I had traffic in that first lap," he explained. "And if I don't do the second one, I'm out.
"He has plenty of pace, so he can afford not to do his second lap. But we were not respecting the delta.
"So, we had to go for the lap, we were plus on the delta, there were three cars queuing, we had to go, or we were going to be illegal, and I already got penalised last race for one of these things.
"So it couldn't happen again. I had no choice, I had to go, so yeah, that was it. The difference between me and Max is he's third, and I'm 17th."
Ocon's frustrating qualifying session came a day after his chassis was badly damaged when he ran over the water valve cover already hit by Carlos Sainz.
Asked by Autosport about his bad luck in a city famous for gambling, Ocon made it clear that he wasn't happy with how his session panned out.
"It's not only Las Vegas, the whole season, I don't seem to catch a break the whole time," he said.
"So it doesn't matter what there is, it's always for us, if it's incidents, if it's problems, whatever it is, it hurts us all the time.
"On the first lap, I got traffic in the worst possible sector, in the last corner, and from Turn 7-9, so I lost some time on that first lap.
"And then on the last lap, obviously, we saw what happened. I lost a good seven-and-a-half tenths or something into Turn 1, and almost did improve by the end.
"It was easily going to be through for us, I think the pace of the car looks promising. And hopefully we can use that tomorrow in the race to catch back up to the field."
