Pakistan clinched the ODI series against Australia by 2-1, the first home series win against the visitors since 1988.
Green shirts were dominant at Gaddafi Stadium as they dismissed Australia for a below-par 210 through their fast bowlers, who shared eight wickets and then chased down the target in 37.5 overs losing just one wicket.
Azam was dropped by Travis Head off Jason Behrendorff on one, took full advantage of the reprieve, driving Marnus Labuschagne for two to complete his 16th ODI hundred off 110 balls.
Babar Azam, who scored 114 in the second game, hit 105 in 115-balls not out on 12 boundaries.
Unbeaten Haq followed his own back-to-back hundreds with a polished 89 for his 11th ODI half-century.
Imam ul Haq hit six boundaries and a six and finished the series with 298 runs.
Scoreboard of the third and final ODI:
T. Head b Shaheen 0
A. Finch lbw b Rauf 0
B. McDermott c Iftikhar b Wasim 36
M. Labuschagne c Iftikhar b Rauf 4
M. Stoinis c Haq b Mahmood 19
A. Carey c Zaman b Iftikhar 56
C. Green b Wasim 34
S. Abbott c Wasim b Rauf 49
J. Behrendorff c Zaman b Shaheen 2
N. Ellis b Wasim 2
A. Zampa not out 0
Extras (lb2, w6) 8
Total (all out; 41.5 overs) 210
Fall of wickets: 1-0 (Head), 2-0 (Finch), 3-6 (Labuschagne), 4-59 (Stoinis), 5-67 (McDermott), 6-148 (Green), 7-155 (Carey), 8-162 (Behrendorff), 9-166 (Ellis), 10-210 (Abbott)
Bowling: Shaheen 8-2-40-2 (w1), Rauf 8.5-1-39-3, Mahmood 8-0-51-1 (w1), Wasim 10-1-40-3, Iftikhar 7-0-38-1
Fakhar Zaman c Labuschagne b Ellis 17
Imam-ul-Haq not out 89
Babar Azam not out 105
Extras (lb1, w2) 3
Total (for one wkt; 37.5 overs) 214
Did not bat: Mohammad Rizwan, Asif Ali, Iftikhar Ahmed, Khushdil Shah, Mohammad Wasim, Shaheen Shah Afridi, Haris Rauf, Zahid Mahmood
Fall of wickets: 1-24 (Zaman)
Bowling: Behrendorff 9-0-51-0, Ellis 6-0-38-1 (w1), Zampa 9-0-50-0, Green 3-0-19-0 (w1), Head 2-0-9-0, Abbott 3-0-15-0. Labuschagne 5.5-0-31-0
Result: Pakistan won by nine wickets
Australia won the first ODI by 88 runs while Pakistan was victorious in the second match by six wickets.
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