Set a target of 243, Australia chased down the total with 4.4 overs to spare in the tri-series opener that also involves New Zealand.
Jacques Kallis and AB de Villiers scored unbeaten half centuries to take South Africa to 244 for two at the close of the fourth day of the second Test against Australia on Monday.
Australia were reeling at 17 for four at the end of the third day in the first Test. A brave century from West Indies batsman Shivnarine Chanderpaul, after he was struck on the head by a Brett Lee bouncer, was the highlight of the hosts' innings of 312 chasing Australia's 431.
'Now the spin that will come will be Glenn Phillips, Rachin Ravindra and Ajaz Patel. You should back yourselves.'
Siraj gave a fiery send-off to Head, who struck his second Test century against India and eighth overall.
Australia fought back in their second innings after losing its top order cheaply to end Day 3 in the first Test against South Africa on 228 for 7, an overall lead of 322, at the WACCA, on Friday.
Phillip Hughes powered to his second century of the match as Australia extended their lead over South Africa to 506 at the close on the third day of the second Test at Kingsmead on Sunday.
IMAGES from the World Cup match between Australia and England played in Ahmedabad on Saturday
Australia vice-captain Michael Clarke returned to the Test team in emphatic style scoring his 14th Test hundred against New Zealand in Wellington.
Ajinkya Rahane and Shardul Thakur led India's spirited fightback, but Australia were sitting in control after stretching their lead to 296 runs at stumps on Day 3.
Rana didn't disappoint Gambhir either as the young pacer grabbed three wickets, supporting skipper Jasprit Bumrah to bundle out Australia for 104 in their first innings.
'You know, there is still a game to go. If we can play that game well, you know, with 2-2, it is a draw. It will be really nice.'
Chasing 413 for victory, Australia were 65 for 2 in their second innings at close on Day 3 of the third Test.
In response, the visitors were 51/4 on a rain-hit third day with questions being raised about batters' technique and the quality of bowling, save for Bumrah.
'We feel slightly behind the game now but there certainly won't be any letting up and certainly won't be any surrendering.'
England were 114 for five in their second innings, just 12 runs ahead on Day 3 of the third Ashes Test.
Images from Day 3 of the first Test between India and Australia, at the VCA Stadium in Nagpur, on Saturday
Australia batted throughout a rain-interrupted third day of the first Ashes Test against England to take a 44-run first innings lead over the hosts on Friday.
Australia repulsed a spirited late charge to record a four-run win over England at the Oval on Friday in the first of seven one-day internationals.
IMAGES from the ICC Champions Trophy Group B match between Afghanistan and England at Gaddafi Stadium, Lahore, on Wednesday.
Australia's fast bowlers, led by man of the match Mitchell Starc, narrowly outshone Pakistan's spinners as Michael Clarke's side edged to a four-wicket win in the opening one-day international of their three-match series in Sharjah. Starc (5-42) and James Pattinson (3-19) were the chief wreckers as Pakistan were bowled out for 198 in the 46th over.
Australia look well on course for a resounding victory over New Zealand in the second Test at Hamilton after the home side were left struggling on 185 for five at stumps at Seddon Park on Tuesday.
Australia, chasing 307 to win, were 212 for four at the close of the fourth day of the first Test against Bangladesh
Australia completed a crushing victory over England in the fourth Test on Sunday to level the Ashes series at 1-1 with one match to play.
Australia batted with grim determination through the final day to earn a draw in the third Ashes Test against England on Monday.
Images from Day 3 of the second Ashes between England and Australia at Lord's.
Australia made a confident start in the third Ashes Test against England as Shane Watson's unbeaten fifty lifted them to 126 for one on a rain-disrupted first day on Thursday.
IMAGES from the ICC World Cup match played between Australia and Pakistan in Bengaluru, on Friday.
Australia stormed to an innings and 99 runs victory, wrapping up a fourth straight win in the series with more than two days remaining.
Australia won the Under-19 cricket World Cup, beating Pakistan by 25 runs in the final at Bert Sutcliffe Oval in Lincoln, New Zealand, on Saturday.
India clinched a comfortable five-wicket win over Australia in the first ODI of the three-match series.
Images from the second semifinal between Australia and South Africa in the ongoing ICC Men's ODI World Cup at the Eden Gardens on Thursday.
Clint McKay took five wickets as Australia's bowlers suffocated Sri Lanka's normally free-scoring batsmen to wrap up the One-day International Tri-series with a 16-run victory in the third and deciding final at the Adelaide Oval on Thursday.
Several batsmen played reckless sweep shots only to fall lbw or be bowled by the Indian spinners.
Australia recovered from a top order collapse in their second innings to end Day 3 in the first Test 307 runs ahead of Pakistan at the MCG on Monday. After dismissing Pakistan for 258 just before tea for a first-innings lead of 196, they were 111 for 3 at stumps.
Cummins had no qualms in admitting that his team was thoroughly outplayed in the series opener but he promised to bounce back in Adelaide
'Hopefully the weather holds off, and then tomorrow it's just about coming in, having a crack, and see where we get to.'
IMAGES from Day 3 of the 3rd Test played between India and Australia in Indore on Friday.
