Initially unaware of the engine issue when it caused him to run wide at Turn 10, Rins re-joined the track action until again feeling the rear tyre slide and this time spotting the fast-growing flames.
Trying to slow his bike as quickly as possible while keeping his feet out of the fire, the Spaniard abandoned ship on the entry to Turn 13.
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"There was a problem with the tube where the oil goes," Rins explained. "In corner 10 I had a small rear slide. I looked down at my boots and the tyre but everything was normal so I continued pushing.
"Then in the next corner I lost it again. So I went out of the line, first for my safety and the safety of the others.
"Then when I saw the bike on fire it was a scary moment because what went into my head was 'Alex, jump' because maybe the bike will explode. So it was not a good moment. But I'm okay."
Johann Zarco fell on the oil but, like Rins, was able to re-join the session after a red-flag period to clean the track.
Suzuki said that the cause of the oil leak is still unclear. Some other bikes have suffered stone damage this weekend.
Rins went on to qualify as the top Suzuki in eighth place, with team-mate Joan Mir down in 18th.
"Difficult," was the word Rins used to describe Sunday's race, "for the conditions, for the heat, for the tyre management. It will be so hard!
"Overtaking will also be difficult because it's only one line and there are not many places to pass. So all the overtakes will be very close with the other riders.
"We need to start well and be as far to the front as possible at the first corner."
The good news is that Rins' physically condition has at least improved after battling sickness on Friday.
"I'm feeling more power in my body, now the problem I have is in the stomach, let's see if the chicken and rice helps me tonight!" he smiled.