Set a challenging 167 for victory at the Dubai International Stadium, Qalanders seemed condemned to an embarrassing defeat when they slumped to 43 for six in the sixth over.
However, the left-handed Narine launched an offensive, hitting 21 from 14 balls in a 45-run, seventh wicket stand off 30 balls with Aamer Yamin who made a run-a-ball 25.
He had struck two fours and a six when he holed out to deep square leg in the 11th over off seamer Wahab Riaz at 88 for seven.
Sohail Tanvir then blasted 36 not out and Yasir Shah, 22, in a 55-run, ninth wicket partnership but they failed to get Qalanders over the line.
Opener Cameron Delport had earlier chipped in with 32 from 15 deliveries.
Opting to bat first, Zalmi were fired by opener Kamran Akmal’s 58 off 40 balls while Bangladesh star Shakib-al-Hasan made 30 from 24 balls.
At the death, Sammy belted a four and a six in scoring an unbeaten 17 off eight deliveries while West Indies batsman Marlon Samuels made 17 in his first appearance of the tournament.
Off-spinner Narine finished with one for 28 from four overs. (CMC)