Shah, a top-order batsman, registered his second fifty of the match after making 98 in Afghanistan's first innings score of 314.
Opener Ihsanullah (65 not out) and Rahmat Shah (76) added 139 runs for the second wicket to make the victory an easy one.
The record still belongs to Australia, who won the first-ever Test match they played against England at Melbourne on March 15, 1877 by 45 runs.
Afghanistan's cricket team claimed a historic first Test win on Monday as they beat Ireland by seven wickets. It's been a long tour, but the lads have been very good. Now we're going to South Africa for World Cup preparation. Before we used to play two-day, three-day cricket and now we are playing the longer form and getting to play Test cricket.
Cricket has become the national sport of Afghanistan, torn apart by decades of war, with numerous Afghan players cutting their cricketing teeth in refugee camps in Pakistan.
Khan, the Indian Premier League (IPL) sensation who is second in the ICC one-day global rankings, played a key role in the Ireland game, taking five wickets on Sunday as Ireland were dismissed for 288.
Nine months since that defeat, the Asian side created yet another history by picking up their first win in the Test match and this time, their opponents were Ireland. "You are never exhausted to play Test cricket, it's always a special feeling", Ireland captain William Porterfield said after the match.
Paceman Yamin Ahmadzai and spinner Mohammad Nabi took three wickets each on the opening day to bowl out Ireland for 172. Afghanistan responded with a total of 314 all out to secure a healthy first innings lead.
"If we'd done how we'd done in the second innings then, it could have been a completely different game".
Afghanistan lost to India inside two days in Bangalore while Ireland went down to Pakistan in Dublin.
Ireland fought back in the second innings by scoring 288, thanks largely to the last-wicket half century stand between Cameron-Dow and Tim Murtagh that set up Afghanistan's target of 147 runs. Still our second game and quite a few players made their debut and I'm sure some of them want to kick-on and contribute more. "But credit to Afghanistan, they outplayed us".