A second half strike from the spot by Michel Otou was enough to hand the Tema-based side a 1-0 away win, ending their 23-game winless run on the road since 2015-16 season.
"We're very happy with the victory over Wa All Stars. It came at a good time since it's our first away win," Kenichi said.
"Many more of this win will surely come as the season progresses because we have a good team. To be clear, this win in Wa is because of our team work and we are hoping to stay together and fight for a common goal," he added.
Allies will now turn attention to regional rivals Hearts of Oak in the Ga derby when they lock horns at the Tema Sports Stadium on May 30.
They will travel to Anyinase to play Karela United in the last game of the first round a week later.