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Islamabad, playing without its four departed overseas players, was restricted to 136-6 after being sent in to bat in a National Stadium empty of fans because of coronavirus fears.
Karachi won with 137-6 in 19.2 overs.
Sharjeel Khan, with 37 from 14 balls, provided Karachi a whirlwind start of 60 runs in the first five overs. But the dismissals of Sharjeel by fast bowler Akif Javed, and Babar Azam, bowled on 19 by paceman Mohammad Musa, helped Islamabad to take the game deep.
Legspinner Shadab Khan grabbed 2-28 to leave Karachi needing 18 off the last two overs.
No. 8 batsman Umaid Asif (13 not out) hit a six off Shadab in the penultimate over, and hit the winning boundary against left-arm seamer Rumman Raees.
Hussain Talat top-scored for Islamabad with 37 and Phil Sault, playing his first PSL game this season, made 25.
Offspinner Iftikhar Ahmed bowled well on a slow pitch and took 1-12 off his three overs as Islamabad struggled to accelerate in the latter half of its innings.
Islamabad, PSL winner in 2016 and 2018, won only three of its 10 league matches and missed the top four places for the first time.
Karachi plays for second on Sunday against Quetta Gladiators in the last league match.