It was a heady atmosphere of dancing and singing in a sea of the ANC's yellow, green and black. But Mr Mbeki, 56, did not waste the opportunity to show that his style will be very different from his predecessor's: he spoke almost exclusively in Xhosa and Zulu, not English.
About 2 million South Africans, out of 18.2 million voters, are still said to be undecided about which party to back. But the ANC looks certain to win about two-thirds of the vote in at least seven of the nine provinces.
"Siyanqoba" (We are winning) was the title given to the rally, at First National Bank stadium, near Soweto. But it was just as much a thank-you to President Mandela. At 80, he has campaigned tirelessly for a smooth transition to Mr Mbeki.
The two looked like father and son as they were cheered around the football pitch on the back of an electric golf cart: the older, greyer President Mandela - patient believer in reconciliation under the South African rainbow - and the shorter, sharper Mr Mbeki, the Sussex University economist with the big idea of an "African Renaissance".
President Mandela spoke first, and in English. He told the crowd "the struggle did not end five years ago" with the country's first multi-race elections. To loud cheers, he said: "It takes more than five years to reverse 350 years of government for the minority."
He said 3 million more South Africans have water than they did five years ago, and he listed other successes, such as the provision of 750,000 new homes, 4 million more people with electricity and 500 new medical clinics. He said the government was winning the battle against joblessless and crime.
Mr Mbeki, who speaks five of South Africa's 11 official languages, continued in a mixture of Xhosa, Zulu - and a little English.
He opened to loud laughter with: "What is wrong with three-thirds?" It was a reference to the claims of opposition parties that if the ANC gets a two-thirds majority it could tamper dangerously with the constitution.
In fact, the ANC needs a 75 per cent vote in parliament to change the constitution. But a big majority would allow it to retire white judges appointed by the apartheid regime.
Mr Mbeki said: "Other parties ask for your votes but after the election they will not be running the country. We want to speed up the pace of change. There is no other party which wants a better life for all."
The upbeat crowd sang: "Don't be jealous [Nelson], the time has come to vote Thabo Mbeki. Wake up everybody, the time has come to vote Thabo Mbeki." The words were from an ANC campaign song by Brenda Fassie.
Many in the crowds said they felt anyone who was voting for any other of the total 26 parties running in national and provincial elections was either churlish or stupid.
"There is no other party," said Stanley Khumalo, 62, a taxi owner, from Boipatong. "People expect so much from the ANC but everything takes time. Crime will drop as soon as we have jobs. We really need the foreign investors to come and give us their investment."
Phillip Malindi, 26 and unemployed, said: "There are 10,500 new homes in Bophelong, the township where I live. People say the apartheid government built better houses than the ANC, but they made us pay for them all our lives. The new houses are not quite so good, not quite so big but at least we have the right to own them."
To many others, such as Elizabeth Mokwena, a retired domestic worker, a vote for the ANC was simply a way to say "a big thank you to Nelson for changing my life".
Mrs Mokwena, from Langa township, has a 500 rands (pounds 50) a month pension and the freedom to go and visit her children. She still remembers the harsh apartheid-era "pass" laws that forbade black people from travelling into areas designated exclusively for the use of whites.
"For the first time, it was only just about six months ago that I caught myself realising I did not have my pass book in my bag and that, actually, it did not matter," she said. "Now it is my right to go to the shops or to go to see my children. Every time I see the police, I do not have to be afraid," she said.
No one seemed very surprised at the lack of white faces in the crowd. One, lone, white South African, Tracey Petersen, said: "The fact that whites are not here does not mean they do not vote for the ANC. Maybe they are afraid to come, maybe it is not their style."
Mr Petersen, a school- teacher, said: "I shall vote for the ANC because it is the only party with integrity. I love Mandela and I think Mbeki will do a good job.
"I hope they get two-thirds of the vote because I feel the government has been held back in the progress it would have liked to make."