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Faulkner took two wickets in his first over, the second of the innings, to have Peshawar in early trouble before Rashid Khan took a pair in the 10th to keep the Qalandars in control.
Rashid returned 5-20 to restrict Peshawar to 160-8, despite Shoaib Malik's 48-ball 73.
In the earlier game, Babar Azam’s unbeaten half century went in vain as Multan Sultans defeated defending champion Karachi Kings by 12 runs.
Azam hit 85 off 63 balls, but Multan held Karachi to 164-7 through some disciplined seam and spin bowling.
After being put into bat, Multan did well in the end to push its total to 176-5 with left-handed Khushdil Shah remaining unbeaten on 44 off 32 balls.
Fast bowler Imran Khan claimed 3-28 and leg-spinner Imran Tahir picked up the key wickets of Martin Guptill and Afghanistan’s Najibullah Zadran, who both scored 11 runs each as Azam was kept in check by the Multan bowlers.
Azam took his time to settle down and got little support from the other end to challenge the target. Azam raised his 18th half century in the PSL off 45 balls but his five fours and four sixes in the end were not enough to carry his team home.
Khan claimed all his three wickets in the last over and was on a hat trick when he dismissed Thisara Perera and captain Imad Wasim off successive deliveries.