The champions, serving temporal home ban arrived in the Capital were hoping to move 13 points clear in the title race with a win over the league debutants, but the Porcupine Warriors were undone in injury time.
Safiu Abdul Fatawu's freekick sailed into the top corner, beating goalkeeper Joseph Addo.
And the win lifts Inter Allies from 14th position to sixth on the log and four points above the relegation zone though the bulk of the matches will be played on Sunday.
Kotoko still maintain their 10-point lead after second-placed Heart of Lions also suffered a 4-1 thrashing in Cape Coast to Ebusua Dwarfs.
The season has four games to go and the Reds need just a win to retain the title.