Image Courtesy: Firoz Ahmed/The Daily Star
The left-arm paceman scythed through the Royals top-order with a sensational spell of seam bowling upfront by snaring four wickets in the Powerplay.
He dismissed Liton Das by a quick in-swinging delivery in the first over of the chase of the modest 159-run target.
Amir then got the wickets of Afif Hossain and Alok Kapali in his second over while Robbie Frylinck removed Ravi Bopara on the other end.
The dangerous Andre Russell was forced to depart for a five-ball duck when he miscued a pull shot leaving the Royals reeling at a perilous 23-5.
Amidst the dismal batting collapse, veteran batsman Shoaib Malik fashioned a sublime countercharge to ignite hopes of a dramatic turnaround.
Malik stitched a 75-run stand with spinner Taijul Islam for the seventh wicket but the climbing asking rate eventually overpowered the duo as they faltered in the death overs.
Malik scored a significant percentage of his team's total, managing to amass a 50-ball 80 laced with 10 boundaries and four sixes before getting out to Amir, who scripted career-best figures of 6-17 in his four-over spell.
Apart from the former Pakistan skipper, only Taijul and Kamrul Islam Rabbi reached double figures as the Royals were bundled out for 131 in 20 overs.
The Russell-led Royals will have another shot at making it to the BPL final when they take on Chattogram Challengers on Wednesday.
Earlier in the game, Nazmul Hossain Shanto struck an undefeated 78 to help the Tigers post an imposing 158-3 despite being initially impaired by a dreadful start.
The Tigers played out two consecutive maiden overs at one stage in the Powerplay with Mohammad Irfan inflicting heavy damage on the top-order.
Shanto then eased into a fluent run-scoring spree and set up a superb batting display to assert their dominance in the game.
Mushfiqur Rahim had to walk off the field retired hurt towards the end but Najibullah Zadran kept the momentum in the Tigers' grasp with a couple of lusty hits.