Rizwan had gone to his eighth IT20 fifty from 38 balls and was keeping Pakistan going with some timely boundaries but lacked the support at the other end.
Rashid ended his spell with the wicket of Shadab Khan (2) before Imad Wasim (3) was run out coming back for a third that would have been straightforward but for some lazy running.
Hasan Ali (15no from 9) gave Rizwan some assistance late on but a superb final over from Chris Jordan cost just five to keep the tourists to a competitive, but gettable, total.
England’s reply followed a similar pattern with Roy flying out of the traps, hitting four boundaries off Shaheen Afridi in the second over, but Jos Buttler was having a rare day where his timing was off.
He had a life on 15 when Maqsood misjudged a chance after Buttler (21) skied one into the overs but he departed later in the Shadab over, another shot sent skywards and Babar was safely underneath it at long off.
As in the Pakistan innings, the spinners were making life extremely difficult for the batsmen. Roy was the exception though, crashing the ball to the boundary nine times and clearing it once on his way to a 30-ball fifty, his sixth in IT20s.
Usman Qadir, brought in for his first appearance of the series, was swept for two more fours by Roy, only for the England opener to change his plan and try to hit the legspinner back over his head, resulting in a straightforward catch for Fakhar at long-off.
With Roy gone, the boundaries dried up with Bairstow (5) and Ali (1) dismissed as they tried to rectify the situation and England found themselves stuck at 112-4 after 15 overs.
Hafeez’s part-time off-spin had been utilised for the first time in the series to allow Pakistan to stick solely with spin from the end of the powerplay until the 18th over, by which stage Morgan and Dawid Malan had brought England to within 19 of victory.
Hasan Ali managed four dot balls in the over as he varied his pace brilliantly but Morgan launched the other two, including the last ball, over the legside for six to bolster his side’s chances.
Hafeez was entrusted with the penultimate over and when he bowled Malan (31), England were still 12 shy with eight balls remaining – far from simple given the conditions.
Livingstone saw it differently, getting down on one knee and clobbering his first ball high over deep midwicket for a huge six to put England firmly in control.
2:00 Stuart Broad was thrilled by England’s dramatic win over Pakistan at Emirates Old Trafford Stuart Broad was thrilled by England’s dramatic win over Pakistan at Emirates Old Trafford
That was his last contribution of the series as he fell next ball trying to finish the job with another maximum, instead handing Hafeez (3-28) his third wicket.
With Morgan on strike, England remained clear favourites but when the captain completely miscued the first ball, sending it high into the Manchester night, it seemed another twist was in the offing, only for Hasan Ali to shell a steepling catch off his own bowling.