Verstappen started the Jeddah race from 15th after a driveshaft failure prevented him from setting a lap time in Q2.
Thanks to Red Bull's majestic pace and a well-timed safety car, the two-time world champion sliced through the field to take second behind team-mate Sergio Perez, who executed a perfect race to win from pole.
But the Dutchman survived another driveshaft scare in the second half on the race after he reported more "strange noises" coming from the rear.
"At one point, I picked up again these vibrations on the driveshaft, on the rear," Verstappen explained.
"The team couldn't see anything, but I'm fairly sure there was something odd going on with the balance since the vibration started to kick in."
When asked if it felt similar to when the driveshaft broke in qualifying, he said: "Yeah, but of course in qualifying it just went. It snapped.
"Luckily, it didn't do that but it started to have a similar effect on the feeling of driving and what you could hear."
Team principal Christian Horner admitted his "heart sank" when Verstappen reported his potential driveshaft issue.
"I think the biggest point of concern for us during the grand prix was when Max radioed in with about 15 laps to go saying he heard a high-pitched noise at high speed," Horner said.
"So your heart immediately sinks, thinking about the driveshaft failure of yesterday.
"But checking all the data that we have here, everything that they could see back in Milton Keynes, all the parameters we had looked okay. And obviously, then they pushed on again. But an amazing recovery from 15th to second."
Verstappen's issue effectively ended any threat he may have wanted to pose to team-mate Perez, as Red Bull ordered both cars to temporarily manage their pace.
Once Red Bull was confident Verstappen's car was fine, it was too late for him to close the gap. Instead, he focused on grabbing the point for the fastest lap, which he took off Perez on the final lap of the race.
"At one point I did the calculations and I wouldn't have been able to close that gap to the end with only 10 laps left," Verstappen said. "So, at one point it's more important to just settle for second, not having an issue with the car."
Red Bull will continue to investigate its driveshaft before the next race in Melbourne, in two weeks' time.
"It's something that we need to understand," Horner added. "We'll take off all the parts. We just need to learn from it going forward, if there's a design tweak or not I don't know. But obviously, we've got four examples of it running in both our car and in the AlphaTauri."
Additional reporting by Jon Noble
