Australia reached 215-6 on the last ball of the 46th over, surpassing England's total of 214 all out from 48 overs at the Sydney Cricket Ground.
England, which won the toss and elected to bat, was led by Jonathon Trott's 84 not out. He was forced to bat conservatively with the tail in an attempt to stretch the innings after the top order had crumbled, leaving England at 130-6 in the 28th over.
Australian fast bowler Brett Lee took three wickets and was voted man of the match.
John Hastings hit the winning runs for Australia and finished unbeaten on 18.
Australia started poorly, slipped to 100-5 with Haddin the only top-five batsman scoring double figures - Shane Watson (9), Shaun Marsh (6), Michael Clarke (9) and Cameron White (7) all failed. But a 63-run stand between Hussey and Steve Smith (26) put Australia back in control.
England's bowlers were led by Chris Tremlett (2-50) and all-rounder Paul Collingwood, who took 2-25 including the wicket of Haddin.
Chris Woakes (1-31), making his one-day international debut, continued Clarke's poor season with the bat, having him caught at midwicket.
Trott posted the only half century for England but his runrate was slowed by the loss of wickets around him.
England sorely missed the presence of South African-born batsman Kevin Pietersen, who was ruled out with a groin injury. He joined England fast bowler Tim Bresnan (calf) and Australian duo Nathan Hauritz (shoulder) and Shaun Tait (thigh) as casualties from Friday's match in Hobart.
Clarke said Hussey's innings showed why he will be a key part of Australia's World Cup campaign, where his side is the three-time defending champion.
"I've said for a long time Dave Hussey's a wonderful player," Clarke said. "It's good to see him finish the innings off today.
"I think with injury concerns with Michael Hussey and also Ricky (Ponting) he's going to play a big role for us throughout the World Cup and he's probably going to bat five or six and be that finisher."
English captain Andrew Strauss said his team's batting effort had not been good enough.
"215 is not enough on a wicket like that," he said. "Jonathan Trott did a good anchor job for us but he needed someone to play and develop a partnership at the other end. Too many of us got to 20 or 30 and didn't go on.
"It's not a time to panic. There's obviously a couple of guys that aren't in brilliant form at the moment but that can change around very quickly."
The fourth match of the series is in Adelaide on Wednesday.
