The Scientific Soccer Lads rode their luck but held on for a deserved 1-1 draw at the Carl Reindorf Park in Dansoman.
Nana Kofi Babil cancelled out Kyei Baffour's opener to leave Medeama with 7 points after three games played.
Liberty opened the scoring through the spot kick after substitute Abraham Wayo was brought down inside the box.
Star man Elvis Kyei-Baffour stepped up and expertly planted the ball into the net after the sending the goalkeeper the wrong way.
Medeama were still much in the game and made promising moves- one of them which was a quick break led to the equalizer.