You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
Cowan departed for 136 in heartbreaking fashion just before the break, run out at the non-striker's end when Dale Steyn got a finger to a Clarke drive and the opener was caught out of his crease backing up.
Australia had resumed on 111-3, 339 behind South Africa's first innings tally of 450, with the tourists keen to get a couple of early wickets to try and force a result in a test which lost an entire day to rain on Friday.
Cowan and his captain Clarke, who was 126 not out at tea, batted with great maturity to dig their country out of a hole, even if the much vaunted South African bowlers failed to get much out of a flat track.
Their partnership was an Australian record for the fourth wicket at the Gabba, beating the 245 Clarke and Mike Hussey made against Sri Lanka in 2007.
Hussey, who had scored one after replacing Cowan at the crease, was set to reprise the partnership with Clarke after tea.
Left-hander Cowan had brought up his fourth test half century with a single to square leg off the third ball of the day and survived a nervous couple of overs in the 90s to go into lunch two runs short of his hundred.
In the second over after resumption, however, the 30-year-old pulled a short Vernon Philander delivery for four to the square leg boundary, beginning his joyous celebrations before the ball hit the rope.
The hundred came from 185 deliveries with 14 fours and was a retort to those critics who have consistently questioned his place in the team since he made his debut in last year's Melbourne test against India.
Clarke, who came to the crease on Sunday with Australia reeling at 40-3, had the first of a string of uncomfortable moments immediately after reaching his 23rd test 50.
Miscuing a pull shot off debutant Rory Kleinveldt, he was mighty relieved when the consequent edge looped over the head of fielder Philander.
Clarke's negotiation of the "nervous nineties" was even more fraught than Cowan's and he was nearly run out going for a second run that would have brought him to the hundred mark.
He survived the scare, however, and a single behind point soon afterwards saw him whip off his helmet to kiss the badge in celebration of a fine innings.
The hundred came in 210 balls with 12 fours and was the 31-year-old's sixth since he took over from Ricky Ponting as test captain after last year's World Cup.
Cowan, meanwhile, had survived a run out scare of his own when he was on 106 before South Africa spurned an even better chance to send him packing when he was on 123.
The Australian skied a hook shot towards long leg and Dale Steyn called for it but was distracted by the approaching Jacques Rudolph and dropped the ball, again depriving Kleinveldt of his maiden test wicket.
South Africa's number one test ranking is on the line in the series, which continues with matches in Adelaide and Perth after Brisbane.