Defending 157, Rishad began tidily but struggled to contain the scoring after that. He eventually finished with 1 for 36 from 3 overs, claiming the wicket of Mohammad Faiq but leaking heavily in the latter part of his spell.
Islamabad chased down 157 comfortably, reaching the target with seven wickets in hand, thanks largely to a brilliant knock from Samir Minhas, who smashed 70 off 36 balls.
The chase got off to a strong start through Minhas and Devon Conway, who added 58 runs for the opening stand. Conway was dismissed for just 6 off 11 balls by Mohammad Amir, but Minhas continued the charge and brought up his half-century in just 25 balls.
The right-hander looked on course for a hundred before falling for a superb 70, an innings laced with 7 fours and 4 sixes.
Rishad finally struck in his third over when Faiq tried to go big and was caught at mid-on by Daryl Mitchell after scoring 19 off 16 balls. However, the Bangladesh spinner conceded 15 runs in the final three deliveries of that over, capping off an expensive spell.
Late cameos from Haider Ali (26 off 16) and Mark Chapman (24 off 7*) then sealed a commanding win for Islamabad.
Earlier, Rawalpindiz posted 156 for 7 after being sent in to bat. Kamran Ghulam top-scored with 50 off 39 balls, while Dian Forrester added a brisk 44 off 19. Abdullah Fazal made 23, and Daryl Mitchell chipped in with 19.
Rishad also got a chance with the bat but could only manage 3 off 6 balls.
For Islamabad, Richard Gleeson, Faheem Ashraf, and Salman Irshad picked up two wickets each.