Coming on to bat at no.3, Shah scored a patient 98 off 214 balls while Asghar Afghan (67) and Hashmatullah Shahidi (61) hit their maiden half-centuries to propel the 'home team' to 314 all out in 106.3 overs in reply to Ireland's paltry first innings score of 172.
Resuming at an overnight score of 90 for two, Shah and Shahidi shared 130 runs for the third wicket to set the platform for a 300-plus total. Shah struck 15 boundaries during his knock while Shahidi hit six boundaries.
Skipper Afghan's 67 came off 92 balls with the help of six boundaries and four hits over the fence.
Ireland: 172 all out and 22 for 1 in 12 overs.
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