After sloppy start to the game, the hosts began to cause troubles for Sharks but their forwards were sluggish up front.
Chelsea finally found their footing and scored the opener by the 10th minute through Stephen Amakonah, who cleverly bent an effort from Collins Ameyaw's free-kick inside Sharks' box.
Four minutes later, Sharks had their first opportunity in the game to pull level, after Benjamin Tweneboah perfectly connected a pass from Felix Addo but the midfielder's effort was saved by goalkeeper Gideon Ahenkorah.
On 38th minute, Isaac Mensah fluffed another opportunity to double the advantage for Chelsea after meeting a teeing cross from Evans Obeng.
By the 53rd minute, Chelsea winger Latif Salifu saw his shot from 20 yards out saved by goalkeeper Joseph Essam while Amankonah bungled the rebound, with the goal at his mercy.
Ten minutes later, Chelsea were handed an advantage after Sharks' defender Ebo Mends brought down Amankona and was shown a second yellow card.
Chelsea tried to make their numerical advantage count but goalkeeper Essam thwarted their efforts.
The visitors pulled level by the 70th minute through Ishmael Hammond who raced down the right flank and delivered a cross to Felix Addo who it dropped in the back net.
Sharks were dealt another blow by the 87th minute after substitute Tanko Mohammed was expulsed for elbowing Zakaria Fusieni.
Chelsea were unable to subdue nine-man Elmina Sharks who defended gallantly to salvage a point.
Sharks have now moved to sixth position on the log with 18 points while Chelsea are 12th with 13.