Blistering half-centuries from Jos Buttler and Jonny Bairstow had laid the foundations in a mammoth chase of 223 but it was Morgan who got England over the line with five wickets and as many balls to spare to seal a 2-1 victory.
He equalled his own England record for the fastest T20 half-century from only 21 balls in an innings containing no fours but seven sixes as England secured their fifth consecutive bilateral series triumph in this format.
Morgan (57no) may have put the finishing touches to the innings but Buttler justified his retention at the top of the order with a fantastic 57 from 29 balls, putting on 91 with Bairstow, who top-scored for England with 64 from only 34 deliveries.
England had successfully chased down 230 against the Proteas in the World T20 four years ago, and this latest effort lays down a marker for the next global sprint format competition in Australia later this year.
Tom Curran, the hero in England's series-levelling victory at Durban on Friday, and Ben Stokes took two wickets apiece and were the only touring bowlers to go at less than 10 an over as South Africa racked up 222 for six.
England knew they had to attack almost from the off and they started well as Buttler took two fours in each of the returning Dale Steyn' s first two overs although Jason Roy edged a booming drive to third man off Lungi Ngidi.
Steyn came in for more punishment from Buttler, who picked a slower ball and clubbed a straight six, before both he and Bairstow did the same to Tabraiz Shamsi with the left-arm wrist-spinner conceding 19 from his first over.
Buttler went to his half-century off 23 balls but Dwaine Pretorius then read the England opener's shuffle across his stumps and a scoop merely went up in the air before being pouched at third man.
Bairstow flayed Shamsi for four-four-six as he brought up his fifty in 27 balls but the boundaries started to dry up thereafter, leading to the Yorkshireman missing a wild swing off Andile Phehlukwayo to be bowled.
Dawid Malan made just 11 on his return to the side in place of the ill Joe Denly before under-edging behind off Shamsi and, although Morgan bludgeoned two sixes in three balls off Pretorius, England were left needing 62 from the final 30 balls.
Another three maximums from Morgan in the space of five balls – one from Steyn and two from Ngidi – ate into the chase as the Irishman took the whip-hand in his partnership with Stokes.
A 61-run union in 4.3 overs was ended when Stokes was caught in the deep off Ngidi, who leaked back-to-back sixes off Morgan which took the England captain to a sensational fifty.
Moeen Ali was dropped on nought before thumping down the ground for four from the first ball of the last over, as England ended their tour of the country on a resounding high.
Earlier on, he conceded 11 in his only over as Temba Bavuma (49) and Quinton de Kock made a rapid start in an 84-run stand.
De Kock struggled with Curran's variations but he would not be subdued for long as he greeted Wood's arrival with a straight six before taking Jordan the distance on three successive occasions.
The 64 South Africa's openers took in the powerplay was remarkably their lowest after six overs in this series before they perished within four balls of each other, De Kock caught at deep midwicket off Stokes for 35 and Bavuma bowled by a quicker delivery that skid on off Rashid.
Rassie van der Dussen mistimed a slower ball from Stokes but Heinrich Klaasen (66) would offer up no such gifts early on, clattering leg-side sixes off England's premier all-rounder, Rashid and Wood as he moved to a 25-ball fifty.
It came as something of a surprise when he got underneath a Curran slower ball which left Stokes with a steepling catch at mid-off but David Miller (35) put the finishing touches to the innings with some lusty blows as Wood took unflattering figures of one for 47 from three overs.