A brace each from Aston Villa striker Jordan Ayew and Rafael Dwamena, coupled with a goal from Majeed Waris and Christian Atsu were enough to break down the resilient opponents.
Coach Kwesi Appiah handed starting role to Aduana Stars goalkeeper Joseph Addo ahead of Richard Ofori and Felix Annan, with Daniel Darkwah, Samuel Sarfo, Rashid Sumaila and Jerry Akaminko making up the defensive setup.
Afriyie Acquah, Isaac Sackey, Yaw Yeboah and Hearts of Oak star Winful Cobbinah completed the midfield, while Frank Acheampong and Jordan Ayew led the attack.
The Black Stars, after containing Asokwa in the opening ten minutes, came close on several occasions to open the scoring but Ayew and Cobbinah's efforts were denied by goalkeeper Samuel Otoo.
However, Ayew finally found a breach in Asokwa's defence by the 17th minute mark and fired in the opening goal before Acheampong made it 2-0 few minutes later.
After the break, coach Appiah changed the entire team for a new set. Goalkeeper Ofori replaced Addo while Harrison Afful, Lumor Agbenyenu, Daniel Amartey and John Boye made up the new defence.
Stuttgart midfielder Ebenezer Ofori, Thomas Teye Partey, Thomas Agyapong and Andre Ayew replaced the midfielders with Majeed Waris and Raphael Dwamena upfront.
Asokwa were able to pull one back against the run of play through former Asante Kotoko striker Emmanuel Osei Carlos by the 49th minute and they subsequently pushed forward in search of the equaliser. However, Warris punished them following a blunder after latching on to a pass from Dwamena by the 52nd minute.
Dwamena turned from a provider to make it 4-1 on 65th minute when he combined with Agbenyenu while Warris added another one four minutes later with a follow up on Dwamena's shot.
With a minute left on the clock, Dwamena capped off an impressive performance with his second goal of the day to make it 6-1 and he received a standing ovation from the supporters.
The Black Stars will continue their preparations at the venue until Saturday and Ethiopia are expected to arrive in Kumasi on Thursday.