Left-hander Shimron Hetmyer again got a start with 30 while Shai Hope got 20, but opener John Campbell (17) failed along with Shamarh Brooks (7).
Hamza Hotak led the attack with three for 59 while fellow left-arm spinner Zia-ur-Rehman picked up two for 54.
Resuming the second day at the Atal Bihari Vajpayee International Stadium on 49 for three, the Board XI started strongly as Ahmadi added 41 for the fourth wicket with Asghar Afghan (10).
But Warrican and Cornwall quickly became acclimatised to conditions and asserted themselves, scything through the middle and lower order as the Board XI lost their seven wickets for 68 runs.
Cornwall looked menacing throughout his 22-over spell and got generous turn while Warrican, who has played seven Tests, demonstrated immaculate control in his 23.1 overs. (CMC)