At the close of the fourth day, Australia were 487 for four in reply to South Africa's 450, a lead of 37 with Clarke unconquered on 218 and Mike Hussey breezing along on 86, giving the home team an outside chance of victory on Tuesday's final day.
"I definitely think we can have a crack at winning. The key is tomorrow morning to be nice and positive and see how we go leading up to lunch, and then give ourselves a couple of sessions to be able to bowl South Africa out," Clarke said.
Australia were in some danger at the start of the day at 111 for three and trailing the Proteas by 339 runs. But Clarke and Cowan laid the foundations for their team's lead with a record 259-run stand for the fourth wicket.
Clarke continued his flourishing batting form as skipper with his 20th Test hundred and his third double century of the year, after his unbeaten 329 and 210 against India at home in January.
He is the highest scorer in Tests this year with 1,000 runs at 111.11 and as Australian captain is averaging over 60 with the bat.His stand with Cowan was the highest fourth-wicket partnership by Australia at the Gabba, surpassing Clarke and Mike Hussey's 245-run effort against Sri Lanka in 2007. It was only ended by a freakish run-out of Cowan for 136 shortly before tea.