Coming out to bat at no.11, Murtagh remained unbeaten on 54 off 75 balls as Ireland top-order batsmen failed to stitch partnerships after opting to bat.
The 87-run last wicket stand between Murtagh and George Dockrell (39) was the only the notable partnership in Ireland's innings which folded up in 60 overs.
Murtagh scored his runs with the help of four boundaries and two hits over the fence.
In reply, Afghanistan ended the day at 90 for two in 31 overs.
Rahmat Shah (22 not out) and Hashmatullah Shahidi (13 not out) were the two unbeaten batsmen at the crease.
Both Ireland and Afghanistan are playing their second Test after making their five-day debut last year.
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