Chasing 242 for victory, Pakistan appeared to be heading towards defeat after England's bowlers reduced them to 154-9 in the 34th over.
However, Shadab launched a superb counter-attack and, with Rauf making an unbeaten seven off 19 balls, guided the hosts to victory with 17 balls to spare. Their 89-run partnership was the highest for the final wicket in a successful ODI run chase.
Earlier, England were bowled out for 241 in 46.4 overs despite Ben Duckett's composed 105. Shaheen Shah Afridi led Pakistan's bowling effort with 4-46 to dismantle England's top order.
The defeat was England's third successive loss in the tri-series after Sri Lanka completed the second-highest successful run chase in ODI history, reaching a target of 430 with one ball to spare.
Afridi struck in the opening over to dismiss Tom Banton before removing Joe Root in the third over, while Jordan Cox fell to Haris Rauf as England slumped to 52-4.
Ben Duckett and Sam Curran steadied the innings with a fifth-wicket partnership of 93. Curran made 42 before becoming Afridi's third victim. Jamie Overton helped take England past 200, while Gus Atkinson finished unbeaten on 36.
Pakistan lost Fakhar Zaman and Babar Azam for 10 apiece before Saad Baig struck a brisk 32 off 22 balls and Salman Ali Agha made 26 to briefly revive the chase. Shadab Khan came to the crease in the 24th over with the hosts struggling at 103-6.
Shadab, who struck 13 fours and five sixes, was given out lbw to Atkinson with 21 runs needed, but successfully reviewed the decision after replays showed an inside edge.