It turned out to be a low-scoring tie with Ki's 28 in third end being the highest score. Deepika shot a 27 in the second end for her best score in the match.
Another South Korean, Hyeonju Choi, secured the bronze defeating America's Jennifer Nichols 6-4 in the third place play-off.
Deepika had beaten Nichols in the semifinals following her win over Miki Kanie of Japan in the last eight stage.