The dashing left-hander hit five boundaries and two sixes in his 72-ball 58 to help Pakistan achieve a revised target of 191 with eight deliveries to spare and take an unassailable 2-0 lead in the five-match series.
Pakistan won the second match at Faisalabad by two wickets after the first match was washed out due to rain at Rawalpindi.
Lendl Simmons hit an attractive 70 before bad light stopped play and technical problems with floodlights caused an hour's delay. It forced the West Indies innings to end at 207-7 after 46.3 overs.
The Pakistan Cricket Board said internal faults disrupted the power supply. The home team's target was revised under the Duckworth-Lewis formula to 191 from 35 overs Sunday.
Pakistan, without their captain Inzamam-ul-Haq, who injured his left little finger while fielding in the morning, got the start they needed with 64 through Farhat and Mohammad Hafeez (31) by the 13th over.
Off-spinner Chris Gayle dismissed Hafeez and then Kamran Akmal (24) but Farhat was in a rampaging mood, hitting and driving to perfection. He was caught off Corey Collymore with 43 needed off 9.5 overs.
Mohammad Yousuf (28) and Shoaib Malik (21) remained unbeaten when the target was achieved.
West Indies, sent in to bat, owed their recovery to Simmons who added 52 for the second wicket with Gayle (41) and 61 for the fourth wicket with Daren Ganga (20) after the tourists lost captain Brian Lara for a first-ball duck.
Simmons, whose 108 for the West Indies 'A' team against touring Pakistan in England four months ago paved his way into the senior team, hit seven boundaries in his 130-ball patient knock before he was bowled by Naved in the 47th over.
Lara, who decided to open the innings, missed a straight delivery from Rana Naved-ul-Hasan and was leg-before for a first ball duck.
Gayle took 13 runs off fast bowler Umar Gul's third over and then took 21 off Naved, including three boundaries and a six to race to 41 off 37 deliveries.
Naved, however, ended Gayle's fiery knock by trapping him leg-before in the eighth over.
Marlon Samuels was unlucky to be given out for 13, caught in the slip by Imran Farhat off paceman Rao Iftikhar when television replays showed the ball touched the ground before Farhat snapped it up.
Left-arm spinner Abdul Rehman struck a double blow by bowling Ganga and then Runako Morton (seven) to finish with 2-33.
Dwayne Smith hit two boundaries and a six in his quickfire 23 and helped Simmons add another 28 for the sixth wicket before Gul removed Smith and Naved accounted for Simmons.
West Indies were forced to keep an unchanged team after key batsman Shivnarine Chanderpaul failed to recover from a knee injury. Pakistan missed vice captain Younis Khan who missed the match due to his brother's death.
Mohammad Yousuf, who missed the second match due to his wife's illness, returned for the only change in the side which played at Faisalabad.
The fourth match is scheduled for Multan on December 13. The fifth and final match will be played in Karachi on December 16.