With England rocking early at 7-2, the tourists applied further pressure this time as Parnell caught Morgan's edge, leaving Quinton de Kock with a simple catch behind the stumps.
Shaking at 15-3 England were unable to show the required steel when they were upended once more when Rabada had Alex Hales loosely driving to put England on the ropes at 15-4.
A horror opening continued to get worse as Rabada picked up his fourth inside a couple of overs having removed both Jos Butler and Adil Rashid in quick succession, leading Morgan to look on in dismay from the pavilion with the home side teetering on 20-6.
Luckily for England, Jonny Bairstow came to the crease with some determined application and he pulled his side out of a dire hole after notching a timely 50, along with some help from debutant Toby Roland-Jones, whose unbeaten 37 helped England limp to 153 all out.
Coming out to bat on a grey afternoon in London, the Proteas made light work of chasing down their minimal total, thanks to a strong opening stand between Hashim Amla (55) and De Kock (34), who were both eventually dismissed by an impressive Roland-Jones.