Hussey scored 65 for his 39th fifty and Maxwell hit a 38-ball 56 not out as Australia successfully chased down a challenging target of 245 in 47 overs, with three wickets in hand, spoiling Pakistan's chances of beating them for the first time since 2002.
Opener Mohammad Hafeez topscored with 78 in Pakistan's fighting total of 244-7 after they were put into bat in Sharjah.
Hussey added an invaluable 51 for the fifth wicket with Matthew Wade (22) after Pakistani spinner Saeed Ajmal (3-37) had threatened to wreck their innings, reducing Australia at one stage to 108-4.
Australian batsman Glenn Maxwell plays a shot. Photo: AFP
Australia had won the first match by four wickets here last week before Pakistan levelled the series with a seven wicket win in the second match in Abu Dhabi on Friday.
But on Monday the 37-year-old Hussey, regarded as one of the best finishers in limited overs cricket, kept his cool during a 72-ball knock. He hit seven fours and a six.
Even when Wade was bowled by Abdur Rehman, Hussey fought hard, adding 67 with Maxwell. When Hussey was bowled by Khan, Australia still needed 19 but Maxwell ensured the chase was successful, hitting four fours and three sixes.
Australian captain Michael Clarke praised the team effort.
"It's fantastic to win the series," said Clarke. "I can't be more proud of the boys because it was tough chase but Michael and Maxwell did very well."
Pakistan captain Misbah-ul Haq said the loss was disappointing.
"It was a hard fought series but in the end we are disappointed with the defeat. We were 20-30 short but full credit to Australia," said Misbah, who has now lost the last three one-day series.
Australia got off to a rapid start with David Hussey putting on 44 by the ninth over with David Warner (21), both taking the attack to the Pakistanis from the outset. David Hussey hit three sixes during his 45-ball knock of 43.
But once Ajmal came on the Australian innings faltered as the off-spinner dismissed David (Hussey), Clarke (32) and George Bailey in his first five-over spell but Hussey then foiled Ajmal in his second spell.
Pakistan were also sloppy in the field as they dropped four catches and their wicket-keeper Kamran Akmal spurned one stumping.
Earlier Hafeez's 97-ball knock -- his first fifty against Australia in eight matches -- helped Pakistan post a challenging total.
Hafeez put on 129 for the opening wicket with Nasir Jamshed (48) and it looked as if Pakistan would post a big total but they were once again derailed by some sustained pace bowling by Mitchell Starc who finished with 4-51.
Jamshed, who hit 97 at Abu Dhabi, was again at his fluent best as he hit six boundaries during his 75-ball knock.
Once Hafeez fell, trapped leg-before by Clarke in the 33rd over Pakistan were hard pressed for runs. Hafeez hit four boundaries and two sixes.
Starc, who took a career best 5-42 in the first match, then came into his own. The lanky left-arm paceman had Asad Shafiq (27) and Umar Akmal (nought) in the same over before ending Misbah's short 25 runs innings in the 47th over.
Azhar Ali made 27 not out to give fillip to Pakistan's total.
Surprisingly, Australia -- considered weak against spin on the Asian pitches -- have lost only one bilateral limited overs series in the sub-continent and Middle East in 20 years. They lost to India in a three-match series in 2010.
Pakistan and Australia now play three Twenty20 internationals -- all in Dubai -- on September 5, 7 and 10.