Haynes hits century as Australia down World Cup holders England
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South Africa also made a winning start to the tournament with a comfortable 32-run victory over Bangladesh in Dunedin.
Haynes and Meg Lanning put on 196 for the second wicket as Australia reached an imposing 310 for three off their 50 overs.
Nat Sciver, with an unbeaten 109 from only 85 deliveries, kept England in with a chance but a target of 36 off the final three overs proved too much.
Haynes said it was difficult to score early in the innings and she was not expecting Australia to reach 300.
"Initially we were thinking 260-270 might be OK, but once we got going we thought let's just try and go as big as we can and to get over than 300 mark was quite important," she said.
England captain Heather Knight took positives from the narrow loss, seeing it as a step up from the recent Ashes series.
"For us as a batting unit that's a real confidence booster," she said.
"It's not the end of the world. We lost the first game of the 2017 World Cup."
Knight won the toss and elected to bowl, removing Alyssa Healy in the ninth over to have Australia one for 35 when Haynes and Lanning came together.
Haynes was the last wicket to fall with her 130 coming off 131 deliveries while Lanning's carefully paced innings produced 86.
After 25 overs Australia were 102 for one with the second half of the innings producing 208 runs.
Tammy Beaumont and Heather Knight put on 91 for England's second wicket and after Knight's dismissal for 40 Nat Sciver dominated the crease.
Australian leg-spinner Alana King, who before the game tweeted her sadness at the death of Shane Warne, took three wickets including Beaumont for 74 before Jess Jonassen's miserly final over took two wickets and ended England's chance.
In Dunedin, South Africa had a comfortable 32-run victory over Bangladesh guided by tight spell of seam bowling by Ayabonga Khaka, who took four for 32.
While the margin was decisive, it was not a convincing performance for South Africa who were all out for 207 on the penultimate delivery.
After a solid 41 from Laura Wolvaardt, the batting faltered to be 119 for five when Marizanne Kapp (42) and Chloe Tryon (39) put on 71 at better than a run-a-ball to lift the total to 190 before the last five wickets fell for 17 runs.
Sharmin Akhter and Shamima Sultana made a solid start for Bangladesh to reach 69 before Sultana went for 27 and Akhter, who was dropped twice early in her innings, was removed soon after for 34.
Nigar Sultana (29) and Ritu Moni (27) put on 53 for the seventh wicket but the required run rate continued to grow and Bangladesh were all out for 175 in the final over.