The Dutchman had opened up a solid lead towards the end of the Monza race, after biding his time early in the grand prix as he battled Ferrari's Carlos Sainz for the win before he moved to the front.
But his hopes of an easy cruise to the flag suffered a late blow when his team came on the radio a few laps from the chequered flag and urged him to back off and not get near a gaggle of backmarkers.
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The team did not specify what the problem was to Verstappen, but they urged him to lift and coast through the lap – which cost him several seconds - and not close in on backmarker Pierre Gasly ahead.
Although the situation prompted a minor bit of drama, Red Bull motorsport advisor Helmut Marko has admitted there was a positive to it, in that it prevented Verstappen from taking some risks of gunning for a late fastest lap.
"It was about the temperatures, to avoid them from going up further," he explained. "We had to keep some of the temperatures within a certain window.
"Max was 12 seconds ahead as well, so there was no reason to push or to take any risks. On the other hand, it was also good because his fastest lap idea couldn't come up."
Red Bull team principal Christian Horner said there was no immediate danger to Verstappen because of the temperatures, but the decision to slow him was based on what would happen if he started following other cars.
"He was managing some temperature issues, and we just didn't want to take any risk," said Horner.
"It was a stinking hot day, and we had a couple of temperatures that were under control, but there was a bunch of cars ahead of [Pierre] Gasly and we just didn't want to run in dirty air. That's why we took it a little bit easier the last few laps."
The late issues on Verstappen's car came at the end of a race that had started with concerns about the Honda power units, following Yuki Tsunoda failing to make the start.
The Japanese driver's AlphaTauri had stopped on the formation lap on the run down to Parabolica, triggering an aborted start for the Italian GP.
With Red Bull running the same Honda engines, there was obviously a risk of any problems Tsunoda had with his power unit impacting the sister team – but this concern was quickly dismissed.
As Marko explained: "We found the cause relatively soon, and that was not something of concern [for Honda], it was something specific for that car."
Additional reporting by Ronald Vording and Filip Cleeren
