Ireland batted first after winning the toss, but struggled to build any momentum as teenager Khan wreaked havoc with his leg-breaks.
Khan, 19, took three wickets for 18 runs while Mohammad Nabi and Gulbuddin Naib took two wickets apiece as Ireland were dismissed for 124 in just 36.1 overs.
It was a paltry target that Afghanistan easily chased down, reaching 127 for the loss of just two wickets inside 24 overs at Stormont.
Ihsanullah Janat top-scored with an unbeaten 57, with the opener accompanied for much of the innings by Hashmatullah Shahidi, whose 34 was the second-highest score of the match.
Afghanistan's victory ensured they took the three-match series 2-1 after winning the opening game by 29 runs on Monday and losing the second by three wickets on Wednesday.
It was a double success for Afghanistan after they also won 2-0 in last week's Twenty20 series against Ireland.
First Published: August 31, 2018, 10:36 PM IST