Uganda took an early lead through Emmanuel Okwi's close-range finish after Zimbabwe goalkeeper George Chigova had parried Lumala Abdu's shot.
But Zimbabwe equalised when Khama Billiat scored after fine work down the left wing from team-mate Ovidy Karuru.
Zimbabwe's Knowledge Musona and Uganda's Patrick Kaddu both missed glorious chances to get a winning goal.
Musona hit the crossbar when faced with an open goal from only four yards out and then, after Zimbabwe's Evans Rusike had a shot saved on the goalline, Kaddu volleyed over from six yards with the goal empty.
Zimbabwe, who were aiming for only their third win at an Cup of Nations finals, now have to beat DR Congo in their final group match on Sunday to have a chance of making it out of the group phase for the first time.
