Both Zaman and Lynn played fantastic knocks to help Lahore Qalandars successfully chase down the 188-run target.
Both Zaman (63) and Lynn (59) made half-centuries to give Qalandars the foundation they needed in the stiff run-chase of 188 before Samit Patel (11*) and David Wiese (17*) played quickfire cameos and took their team past the finish line in the final over.
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Zalmi captain Wahab Riaz (1/27) delivered an economical spell while Carlos Brathwaite (3/28) bagged three wickets but their effort proved insignificant in the second half.
Earlier on, fifties from Shoaib Malik (62) and Haider Ali (69) took Peshawar to a mammoth total of 187/7.
Shaheen Afridi (3/28) bowled a fantastic spell but the rest of the Qalandars attack proved expansive.
With this victory against the second-ranked Zalmi side, Qalandars reached third in the points table with four wins and as many losses.
Brief Scores:
Peshawar Zalmi 187/7 in 20 overs (Haider Ali 69, Shoaib Malik 62; Shaheen Afridi 3/28) lost to Lahore Qalandars 189/5 in 19.5 overs (Fakhar Zaman 63, Chris Lynn 59; Carlos Brathwaite 3/28) by five wickets