For the second game in a row the hosts strangled their opponents with spin, Rashid twirling his way to 4-35 and Moeen Ali with a miserly one for 19 as Pakistan spluttered to 154-6.
A flurry from Jason Roy (64 in 36 balls) made England firm favourites but Pakistan dragged it back with regular wickets and it fell to number eight Chris Jordan to sprint through for the winning runs with just two deliveries and three wickets remaining.
Returning captain Eoin Morgan had chipped in with a rapid 21 as pressure peaked at the death, while rising star Liam Livingstone faced just two deliveries – smashing one for six, out to the other.
Victory meant a 2-1 scoreline in England’s favour and ensured they have now won all four of their limited-overs series in recent weeks.
Batting first Pakistan made 40 off their first five overs, with Mohammad Rizwan finding his range early with sixes off Saqib Mahmood and Jordan.
But his partner, the ever dependable Babar Azam, was not himself, struggling for timing, struggling for strike and ultimately struggling to pick Rashid’s googly as he fell to a textbook stumping.
Sohaib Maqsood started confidently, sending two of his first four balls from Rashid to the ropes, but when the battle resumed after a change of ends the result was decisive.
Looking for a big blow down the ground, Maqsood could only pick out Roy at long-on.
Even when Rashid got it wrong he got it right, with middle-order veteran Mohammad Hafeez flailing a drag down straight to his White Rose colleague Jonny Bairstow at deep square-leg three balls later.
Pakistan had drifted to 69-3 in the ninth, with one man to blame for their plight.
Rizwan was unaffected, carrying his bat for 76 not out, but with the ball gripping Moeen and Livingstone assumed full control.
Moeen worked through his four overs of precise off-breaks without a single boundary conceded, crowning his miserly spell with an lbw against Fakhar Zaman (24).
Surprisingly, Rashid had never taken four wickets in a T20 International before but rectified that with his final delivery as Shadab Khan holed out.
After a careful start against Imad Wasim’s spin, Roy made a statement by taking four boundaries off Shaheen Shah Afridi’s opening over, using a persuasive combination of power and placement.
Jos Buttler was struggling at the other end, botching two attempted paddles off Hasan Ali and dragging Imad past his leg stump, before Roy set things straight with a straight six and a swept four off the spinner.
England looked to be cruising when Roy showed off sweeps on both sides of the wicket to pilfer 15 from Usman Qadir’s first over, but it was not a done deal yet.
First came the mercy killing of Buttler on 21, an untidy knock ending with an untidy hack off Shadab, and then the vital wicket of Roy.
A series of perfect sweeps had carried him to a 30-ball half-century and beyond but he lost focus and lofted Qadir sky high to long-off with 63 still required. Suddenly they needed a calm head.
Neither Bairstow nor Moeen could oblige, one failing to clear mid-off, the other bowled by Hafeez on a wild charge. With four overs left 39 were needed, and with three remaining that was down to 29.
Enter Morgan, who had sent himself in ahead of man-of-the-moment Livingstone.
Twice he picked his moment against Hasan Ali and twice he sent the ball spiralling into the stands for six. That should have been enough but the end was pure drama. Yorkshire’s Dawid Malan, who never got going in his 31, was clean bowled by Hafeez, allowing Livingstone to make his remarkable, brief cameo. After swatting the spinner for miles from his first ball, he sprayed the next to short third man.
Even Morgan could not rise above the tension, held in the deep immediately after being dropped, but two hard run twos from Jordan’s bat settled matters.
After the win, Morgan said: It means a huge amount. The style in which we play naturally, this is the worst type of wicket for us to apply it on – so it’s a very proud day for us to do it on a spinning, slow wicket against a very good side.
Batting hero Roy, added: “It was a little bit difficult out there, you had to have a pretty strict game plan. I was lazy again with the dismissal – which is pretty frustrating, three games in a row.
“But for us to have a performance like that, on a pitch like that is very rewarding. We play incredible cricket on flat pitches, scoring millions of runs, but when the ball and the pitches are a little bit slower we have struggled in the past, so today will give us a huge amount of confidence.”