After Nicole Bolton, Alyssa Healy and Ellyse Perry struck half-centuries, Haynes took the game away from England by blasting an unbeaten 89 off just 56 balls to lift the hosts to 296-6, having lost the toss.
England, faced with a revised target of 285 from 46 overs, were never at the races and were dismissed for 209, despite a maiden ODI half-century from No 7 Barnsley all-rounder Katherine Brunt.
Australia’s second consecutive victory gave them a four-point lead in the multi-format series, meaning they only need another four from the remaining ODI, one-off day/night Test and three Twenty20s to retain the Ashes.
Heather Knight’s decision to bowl first soon backfired as Bolton and Healy racked up an opening partnership of 98 in 20 overs.
Haynes hit nine fours and three sixes as Australia bludgeoned 94 off the final 10 overs, with Jenny Gunn taking two late wickets to finish with 4-55.
England were soon in trouble at 20-2 and slipped to 91-5 and were left requiring 149 from the final 16 overs.
Brunt blasted her side’s first six in the 35th over en route to a battling 54-ball 52 before being bowled by Megan Schutt, who finished with 4-26.