Despite the draw the Algerians have confirmed their place at the next Africa Cup of Nations finals in Cameroon, which have been delayed until 2022.
After goals in the 34th and 38th minutes, including a fine solo effort from Riyad Mahrez, it looked like Algeria would make it four wins from four.
In the 34th Reda Halaimia whipped in a long cross from the right and an unmarked Andy Delort had a straightforward header to score his first goal for Algeria.
Moments later came the brilliance from Manchester City’s Mahrez as he flicked the ball past one defender and then cut into the area before twisting and turning to wrong-foot two defenders and firing home.
The Warriors pulled a goal back two minutes before half-time as striker Knowledge Musona curled in a free kick from the edge of the area to beat Rais M’Bolhi.
That seemed to galvanize Zimbabwe and they created the better chances after the break and were rewarded when Tanzania-based Prince Dube scored the equaliser in the 82nd minute seconds after coming on as a replacement.
He picked up the ball as it was flicked on from a corner and his shot somehow went over the line as M’Bolhi failed to hold the ball for what looked like a routine save.
It was a big improvement from Zimbabwe who had lost 3-1 to Algeria on Thursday evening.
In the days other Group H match there was a surprise 1-0 win for Botswana over the visiting 2012 Nations Cup winners Zambia.
The only goal of the game came after just six minutes played through Mosha Gaolaolwe, who plays his football in the second-tier of South African football.
Algeria top the group with 10 points, with Zimbabwe five points behind, Botswana are up to third with four and Zambia are once again bottom on three.