It was Afghanistan's first ODI victory against Pakistan in eight attempts and the outcome leaves defending champions England at the bottom of the points table.
"This win tastes nice," a beaming Shahidi said after their second victory in five matches.
Teenage spinner Noor Ahmad (3-49) dismissed Abdullah Shafique (58) and Mohammad Rizwan (eight) in his successive overs in his memorable World Cup debut.
Shaheen Afridi returned to break the burgeoning stand, dismissing Gurbaz, but Zadran and Rahmat Shah, who made 77 not out, continued the good work.
Hasan Ali ended Zadran's gallant knock but Shah and Shahidi milked the Pakistan attack with consummate ease during their unbroken 96-run stand to seal a memorable victory over their neighbours.
Persons:
Afghanistan's Ibrahim Zadran, Samuel Rajkumar, Hashmatullah Shahidi, Babar Azam, Abdullah Shafique, Shahidi, Babar, Haq, Noor Ahmad, Mohammad Rizwan, Noor, Iftikhar Ahmed, Shadab Khan, Iftikhar clobbered, Shadab, Rahmanullah Gurbaz, Ibrahim Zadran, Shaheen Afridi, Gurbaz, Rahmat Shah, Hasan Ali, Amlan Chakraborty, Ken Ferris
Organizations:
Cricket, ICC Cricket, Chidambaram, REUTERS, Rights, Pakistan, England, Thomson
Locations:
Pakistan, Afghanistan, Chennai, India, Rights CHENNAI, New Delhi