Noman and Sajid knocked over all 10 England wickets to dismiss the visitors for 112 before Pakistan raced to victory in Rawalpindi before lunch on day three of the third Test.
Shan Masood hammered five boundaries in six balls, launching Shoaib Bashir over the ropes to complete a resounding victory, his first series triumph as captain.
Noman finished with figures of 6-42 and Sajid 4-69 after England resumed the day on 24-3 but were dismissed in 37.2 overs for their lowest total in Pakistan.
England won the first Test by an innings and 47 runs while Pakistan took the second by 152 runs, both in Multan.
Pakistan lost opener Saim Ayub for eight but Masood’s six-ball 23 not out ended the match.
The Pakistan captain had lost his previous two series in charge — 3-0 to Australia and 2-0 to Bangladesh — since being appointed last year.
Noman and Sajid were brought into the line-up after England destroyed the hosts in the first Test in Multan by an innings and 47 runs.
The duo have knocked over 39 wickets between them in the subsequent two Tests, turning what looked like an easy England series victory Pakistan’s way.
Joe Root top-scored with 33 while none of the other England batters could last long enough to stop Pakistan’s charge toward a first home series win since beating South Africa in February 2021.
England’s previous lowest total was 130 in Lahore in 1987.
England’s fate was sealed once Noman dismissed overnight batsman Harry Brook caught behind by Mohammad Rizwan for 26 and skipper Ben Stokes leg-before for three.
Stokes once again fell bizarrely as he offered no stroke to a Noman delivery, expecting it to go down the leg side but it struck him in front of the stumps. England skipper, who missed the first Test with a hamstring injury, managed just 53 runs in four innings.
Sajid made it 6-75, dismissing Jamie Smith who tried to hit him out of the ground only to miss the ball and lose his stumps for three.
Noman completed his sixth five-wicket haul when Root edged a sharp turning delivery to Rizwan, quashing all hopes of an England fightback.
Sajid dismissed Rehan Ahmed for seven while Noman wrapped up the innings with the wicket of Jack Leach, who bowled for ten.