Keen to bounce back from a series-opening loss to the hosts on Friday, South Africa were sent into the field by George Bailey, captaining Australia on Sunday after Michael Clarke was ruled out of the series with a hamstring injury.
Career-best figures from man-of-the-match Morkel (5-21) and an effective cameo from Dale Steyn (3-35) saw Australia bowled out for a paltry 154.
While some inspired bowling from Josh Hazlewood (5-31) gave the hosts a chance, it was a case of having simply too few runs on the board as Proteas captain AB de Villiers (48) steered his side to victory.
The best-of-five series is now evenly poised at one win apiece, with the two sides set to face off again in Canberra on Wednesday.
Despite the Perth wicket looking batter-friendly, the Australia top order faltered - David Warner fell in the first over, gloving a vicious Morkel bouncer to wicketkeeper Quinton de Kock for a duck.
The wickets kept tumbling as Aaron Finch (8), Shane Watson (11) and Steve Smith (10) all departed in swift succession to leave Australia reeling at 34-4.
Playing in front of his home crowd, Mitchell Marsh gave the Australian scorecard some respectability as he combined with Bailey for a 58-run fourth-wicket partnership before the captain fell to Vernon Philander (1-16) for 25.
Morkel continued to do damage, removing Matthew Wade (19) and Glenn Maxwell (0) within three deliveries before stunting Mitchell Johnson's boundary-hitting potential in his next over, seeing the left-hander caught behind for just two
With Marsh running out of partners, the young batsman went on the offensive, eventually falling to Steyn for a brave 67 - Morkel taking a second catch of the innings - to bring Australia's innings to a close.
Though the Proteas were chasing a modest total, they too started nervously as De Kock departed for just four, brilliantly caught by Watson in the slips off Hazlewood in the second over, and Hashim Amla's 100th ODI ended in disappointment as he edged Johnson to Wade for a ponderous 10.
That left the tourists on 21-2 but, unlike Australia before them, they had batsmen to steady the ship as Rilee Rossouw (30) and Faf Du Plessis (19) put on 43 before the former's dismissal brought De Villiers to the crease.
The recently crowned ODI Player of the Year went on the offensive from the outset, cashing in on Johnson in particular as he put his side firmly in the driver's seat despite Hazlewood taking Du Plessis and Farhaan Behardien in consecutive deliveries.
By the time De Villiers charged down the wicket to Hazlewood, throwing away his wicket just short of 50, South Africa were 141-1 and cruising to an easy win which was safely negotiated by some sensible stroke-play from David Miller (22) and a no-nonsense boundary from Steyn.