Tail-ender Hunain Shah came in to face the final ball after the dismissal of Naseem Shah and steered fast bowler Mohammad Ali's delivery through point to clinch the nail-biting decider.
Multan were restricted to 9-159 on a spinners' paradise, with Islamabad allrounder Imad Wasim grabbing 5-23 and captain Shadab Khan picking up 3-32.
"The sign of a good team is they win even without playing a perfect game," said Shadab, who was named player of the league after scoring 305 runs and taking 14 wickets.
Islamabad's chase got a great start from their opener Martin Guptill, stumbled in the middle but finished strongly from Wasim (19 not out) and Naseem (17).
They reached 8-163 to add to their PSL titles from 2016 and 2018.
"To pick up a five-for in a final and to stay in (batting) during a crucial game, it was a new experience," Wasim said.
"We should have finished the game earlier rather than taking it down to the wire. I'm glad Hunain finished it."
It was heartbreaking for Multan, who lost last year's final to Lahore Qalandars by one run.
Playing their fourth consecutive final, the Sultans had won the group stage and were the favourites for the showpiece game.
Islamabad gained momentum in the play-offs, thanks mainly to Wasim's brilliant all-round show.
New Zealander Guptill hit a 30-ball half-century before he was run out in the 13th over with his side at 4-102.
Multan kept coming back strongly through spinners Khushdil Shah (2-21) and Iftikhar Ahmed (2-19).
League-leading wicket-taker Usama Mir, who finished the competition with 23 wickets, dismissed dangerman Azam Khan for 30 in the death overs.
When Ahmed plucked a superb return catch off Faheem Ashraf at 7-129, Islamabad still needed 31 off the last 17 balls.
Naseem smashed a quickfire 17 off nine balls and Imad kept his cool to guide Islamabad to a sensational two-wicket win.
Imad had earlier wrecked Multan's top order with the wickets of Yasir Khan and David Willey in his first over.
In-form Usman Khan revived Multan hopes with a gritty 57 off 40 balls before Wasim struck back in the middle overs by dismissing Johnson Charles (four).
Wasim capped his brilliant display with the wickets of Khushdil Shah (11) and Chris Jordan (duck) in his final over.
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