Shah struck five boundaries during his 90-ball knock of 72 and added 50 for the second wicket with Ihsanullah Janat (45) after Afghanistan won the toss and opted to bat on a flat pitch.
Janat hit six boundaries in his 65-ball innings while his opening partner Mohammad Shahzad batted in his aggressive style, hitting a six and four boundaries in his 47-ball 34.
For Sri Lanka, who lost the opening match to Bangladesh by 137 runs in Dubai, seamer Thisara Perera took five for 55 and spinner Akila Dananjaya finished with two for 39.
Defending champions India, Pakistan and qualifier Hong Kong are placed in Group A.
Pakistan beat Hong Kong by eight wickets in Dubai on Sunday.
Top two teams from each group will qualify for the Super Four stages from where top two teams will play the final in Dubai on September 28.