The hosts took a fifth-minute lead through David Omengo, who headed in a long throw. The power men thought they had sealed the win, but Enosh Ochieng slotted late to hand the Soldiers a point.
The draw left Ulinzi Stars 12th on the log with 15 points while Stima is sixth in position with 20 points.
Mathare United, who will play Sofapaka on Tuesday, lead the log with 25 points, three more than defending champions Gor Mahia, former champions Tusker and Bandari. Bottom three is occupied by Chemelil Sugar, Mt. Kenya United and Posta Rangers.