Trump had appeared in control at 9-7 overnight and strengthened his position with an opening break of 77. But the match turned abruptly as his fluency deserted him. Vafei, composed and persistent, chipped away at the deficit, capitalising on a series of missed chances to draw level at 10-10.
Momentum swings to Vafei
The Iranian’s confidence grew as Trump’s certainty faded. A run of four consecutive frames, built on contributions of 53, 55 and 77, carried Vafei into the lead for the first time since the early stages of the match.
Trump responded with a break of 76 to restore parity at 11-11, and when Vafei faltered in the next frame, the world number one punished him with 64 to move within one of victory at 12-11.
With elimination looming, Vafei produced his finest contribution -- a superb 106 that forced a decider and shifted the pressure squarely back onto Trump.
Decider drama settles contest
The final frame encapsulated the contest, as Trump fashioned the first opportunity but could make only 21 before losing position, and a series of loose safety exchanges handed Vafei his chance.
A break of 91, built on precise potting and calm decision-making, carried him to a famous victory, prompting an emotional reaction as the Crucible crowd rose in appreciation.
Vafei now moves into a quarter-final meeting with Wu Yize.
Robertson cruises into quarter-finals
There was little drama for Robertson, who efficiently converted his overnight advantage to book his place in the last eight.
After a scrappy opening frame that went to Wakelin, the Australian took control with a tidy 104 and never looked back. Smaller contributions proved sufficient to edge him to the brink before a break of 82 sealed the match at 13-7.
Robertson will next face John Higgins, who earlier eliminated Ronnie O'Sullivan.