Australia and Pakistan squeezed into the World Twenty20 semi-finals on Tuesday as India and South Africa packed their bags after a topsy-turvy last round of Super Eight matches. On an evening when run-rate calculations were paramount, Australia lost to Pakistan but still went through, while former champions India headed home despite eking out a narrow, one-run win over South Africa. Pakistan, the 2009 winners, will take on Sri Lanka in Thursday’s first semi-final at Colombo’s Premadasa stadium, while Australia clash with the West Indies on Friday at the same venue. The final will be played on Sunday. In Tuesday’s first match Australia, the dominant team in group two with two successive wins, crashed to a surprise 32-run defeat to Pakistan after a five-man spin attack restricted them to 117-7 on a slow wicket. India’s victory over winless South Africa later left them level with Australia and Pakistan on four points each, but a poor net run-rate ended the 2007 champions’ campaign. India, who scored 152-6, needed to keep South Africa below 122 to go ahead of Pakistan’s run-rate, but the Proteas rode on a 38-ball 65 from Faf du Plessis to make 151 all out. George Bailey’s Australia took the top spot in the group with a net run-rate of 0.46 against Pakistan’s 0.27, while India were third at -0.29. Indian captain Mahendra Singh Dhoni said the nine-wicket defeat in the rain-affected game against Australia cost his team dearly. “If you take that Australia game out, we performed brilliantly,” said Dhoni. “Overall I am quite happy with how the team performed, but there were instances when we should have had 10-15 runs more on the board.” South African captain AB de Villiers was devastated by the loss of all three games in the Super Eights. “Disappointed is not the word to describe it, we’ve had a poor tournament,” said de Villiers. “We’ve let the country down and that’s what hurts the most. “We did all the preparations possible, we thought we were ready, but the guys didn’t click.” Pakistan’s prolific spinner Saeed Ajmal claimed 3-17, but it was 20-year-old Raza Hasan who was declared man of the match against Australia for conceding just 14 runs and taking two wickets in four overs of steady left-arm spin. “I am grateful to see the effort put up by the boys today,” said Pakistan captain Mohammad Hafeez. “It was a big game for us and we needed to be at our best against a side like Australia. “Once we got a good total, we knew we will do well because there was going to be help for the bowlers. Raza Hasan was brilliant, a great find for us.” Australia, who have never won the World Twenty20 despite taking four World Cup titles in the 50-over game, had breezed through four consecutive matches in the tournament before being halted by Pakistan. “Pakistan outplayed us,” Bailey admitted. “The ball turned a lot more than before and they used spin against us very well. “The challenge for us now will be to get the winning form back in the semis.” Veteran Mike Hussey was Australia’s mainstay with an unbeaten 54 off 47 balls, as none of the other batsmen managed to cross 15 against the rampaging spinners. Australia, who needed to make 112 or more to qualify, achieved the target when Hussey cut seamer Umar Gul to the fence off the first ball of the final over. Gul’s two overs at the end were the only ones by a seamer as the spinners shared 18 overs between themselves. Pakistan’s innings revolved around left-hander Nasir Jamshed’s 55 off 46 balls, which contained four boundaries and two sixes.