South Africa reached 270 for seven to secure victory with 21 balls remaining in the match.
South Africa had looked to be struggling as they took their score to 209 for six in the 40th over still needing 61 runs to win off 31 balls.
Morkel made light work of the victory target as he smashed six fours and a six to take South Africa to within five runs of success before he was well caught by a sprawling James Hopes at a wide long-on off the bowling of off spinner Nathan Hauritz.
Johan Botha then ended the match in some style as he drove fast bowler Shaun Tait through the covers for four.
After the early loss of Hashim Amla, courtesy of a run-out, Herschelle Gibbs and Jacques Kallis put on a 96-run second wicket partnership to provide the South African run-chase with a solid base.
During his knock Kallis became the first South African, and the fourth player in history, to pass 10 000 ODI runs.
Gibbs played an innings of class as he notched up his 36th one-day international half-century before he played away from his body to a wide delivery from left-arm seamer Mitchell Johnson to steer a catch to Mike Hussey at first slip. Gibbs was out for 64 off 52 balls with 10 fours and a six.
Kallis continued on his way, reaching his 70th ODI half-century, before he tried to force a back foot drive off the bowling of Tait only to feather a catch through to keeper Brad Haddin to be dismissed for 60 off 72 balls.
Kallis dismissal ended a passage of play where South Africa lost four wickets for 38 runs but Mark Boucher, 31 not out, and Neil McKenzie steadied the innings with a sixth-wicket partnership of 46 before Morkel's heroics.
Left-arm seamer Nathan Bracken, who snared his 150th ODI wicket during the match, impressed for Australia. At one stage he boasted figures of one for 10 off six overs before finishing with one for 29 off nine overs.
Earlier, South Africa's bowlers fought back well to bowl Australia out for 269.
Australia had got off to a rollicking start as David Warner and Shaun Marsh put on 114 runs for the first wicket, off 18.5 overs, with Warner playing an aggressive innings.
The left-handed opening batsman clubbed 69 off 60 balls with six fours and two sixes, his maiden one-day international half-century, before he swung across the line to be clean bowled by a full delivery from fast bowler Dale Steyn.
South Africa's fast bowlers had taken a terrible pounding from Australia's batsmen but the introduction of spin, in the form of off spinner Botha, had the desired effect for the Proteas as Botha had Marsh stumped by keeper Boucher.
Marsh departed for 43 off 63 balls and Botha continued to torment the Australian batsmen as he removed Ricky Ponting and Brad Haddin to finish with the impressive figures of three for 32 off 10 overs.
Australia lost their last four wickets for the addition of 30 runs as the home-side was dismissed with four balls of their allotted 50 overs remaining.
Australia - Shaun Marsh, David Warner, Ricky Ponting (capt), Michael Hussey, David Hussey, Brad Haddin (wk), James Hopes, Nathan Hauritz, Mitchell Johnson, Nathan Bracken, Shaun Tait
South Africa - Herschelle Gibbs, Hashim Amla, Jacques Kallis, Neil McKenzie, JP Duminy, AB de Villiers, Mark Boucher (wk), Albie Morkel, Johan Botha (capt), Dale Steyn, Makhaya Ntini
