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The two left-handers put on 72 without loss off 19 overs to give the Australians a flying start as they chase 241 at Hobart's Bellerive Oval to wrap up a two-nil series win over the Black Caps.
Australia thrashed New Zealand by nine wickets in the first Test in Brisbane last weekend.
No play was possible after tea, with Warner on 47 off 50 balls with eight boundaries and a concentrated Hughes not out 20 from 64 deliveries.
Australia will push for victory on Monday's fourth day, needing 169 more runs with all 10 wickets intact.
"I thought both openers did a fantastic job, it's been hard work batting up the top of the order with that new ball and I thought they applied themselves well," Australian vice-captain Brad Haddin said.
"They hit the ball there that needed to be hit, but they also left well which I think is important, especially with the left-handers out there to Chris Martin, to leave well."
A total of 30 wickets have fallen in the eight of sessions play in a Hobart Test where the ball has dominated the bat.
Neither opener had too many troubles, although "Hot Spot" replays suggested Hughes may have gloved a leg-side catch to wicketkeeper Reece Young in the third over before he had scored, but the Kiwis did not seek a review.
Hughes is seeking a big innings to ease pressure on his Test spot after falling cheaply to Martin three times in the series.
The Kiwis, leading by 14 runs on the first innings, lost seven wickets for 87 in the extended morning session to be all out for 226 at lunch after resuming the day on 139.
"We have to start really well tomorrow, there's been a little bit of assistance in the wicket throughout the game so we know that will certainly be there tomorrow morning," said Black Caps bowling coach Damien Wright.
"Bellerive traditionally over the years offers a little bit in the mornings and it's really important for us to break this partnership and get early wickets."
James Pattinson (3-54), Peter Siddle (3-66) and spinner Nathan Lyon (3-25) shared the wickets as the Black Caps unravelled after losing skipper Ross Taylor and Dean Brownlie.
Taylor top-scored with 56 off 169 balls but once he and first innings top-scorer Brownlie (21), the Kiwi innings crumbled as they sought to set a match-winning fourth innings total.
"They were playing well, but we knew if we could build enough pressure on them we felt they would crack before us and they did," Haddin said.
Kane Williamson was out on the third ball of the day, brilliantly caught by a diving Ricky Ponting at second slip off Siddle for 34.
Pattinson dropped a sharp caught and bowled chance off Taylor before the Kiwi captain brought up his 15th Test half-century off the next ball.
But the bowler had his revenge in the 63rd over when he enticed Taylor to nick an out-swinger to Michael Clarke at first slip.
Brownlie tried to get out of the way of a Pattinson bouncer only to be caught behind off the back of his bat for 21.
Without the steadying influence of the injured Daniel Vettori, the New Zealand tail folded, with Tim Southee (13), Doug Bracewell (4) and Trent Boult (21) all out irresponsibly slogging spinner Lyon.
