Rudolf Mensah scored a last-gasp strike to settle the match in favour of the Scientific Soccer Lads.
After a drab first half, Dwarfs broke the deadlock courtesy substitute Seidu Abubakar in the 69th minute.
The lead stood for only four minutes as Liberty restored parity. Alhassan Mubarak scored in the 73rd minute.
With the game drawing for a close, Rudolf Mensah popped up to net the winner for Liberty.
The win is Liberty's first of the season.
For Ebusua Dwarfs, it is their fourth straight defeat in the competition. Read Full Story
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