Six hours after Ronnie O'Sullivan was also sent packing 13-12 by John Higgins, Vafaei reeled in a 9-7 overnight deficit then turned on the style when it mattered as breaks of 106 and 91 edged him over the line.
It was the same old story for World No. 1 Trump, who is still searching for his second title after his initial breakthrough in 2011, as he squandered a hatful of chances including a 25-point lead in the decider when he had looked a heavy favorite to reach the last eight, ESPN reported.
Vafaei will next face China's rising star Wu Yize, who also contributed to a day of upsets by sinking four-time champion Mark Selby 13-11.
And as the big names continue to scatter, the Iranian world number 32 is adamant he has every chance of continuing his run deeper in the tournament, insisting: "Some of us are different. When you see the line you get hungry or you get tired, it's up to you.”
"I was enjoying every moment of it. I was born for this kind of situation. If I don't take this kind of chance I will never become world champion. Every day the Crucible trophy is living in my head rent free," the Iranian player stated.