Goals from Baghdad Bounedjah, Sofiane Feghouli and skipper Riyad Mahrez gave the Algerians a comfortable lead, before Tino Kadewere pulled one back for The Warriors with 12 minutes left on the clock.
The victory sees Algeria retain their hold on top of Group H with a maximum nine points and put their journey to Cameroon for a title retention plot intact. Zimbabwe remain second with four points while Zambia moved to third after earlier beating Botswana who drop to bottom of the pile.
The reigning African champions were patient in their approach and let Zimbabwe do all the early chasing of chances. Zdravko Logarusic’s men had an opportunity as early as the second minute when a poorly defended freekick landed on Khama Billiat on the right.
However, the pint-sized forward was denied by keeper Rais Mbolhi who stuck out a foot to block the low effort for a corner.
On the quarter-hour mark, Zimbabwe had an even better chance when a freekick floated by skipper Knowledge Musona landed on Tino Kadewere’s head, but the forward’s glancing effort with the keeper beaten flew over the bar.
All this time the Desert Foxes were slowly growing into the game and they began to ask more questions to Zimbabwe in the final third.
On the half-hour mark, Bounedjah had a chance when he was sent through by a pass from Mahrez, but he took a tumble as he went for the shot, the ball only slowly gliding into the keeper’s waiting gloves.
The Qatari based forward broke the deadlock with a low finish after reacting quickest when keeper Elvis Chipezeze spilled a Sofiane Feghouli shot after the Algerians swiftly turned defense into offense.
Two minutes to the break Algeria doubled their lead when Feghouli turned from provider to scorer, diving to head the ball home after being picked out by a brilliant Mahrez cross.
Zimbabwe started the second half with a change, keeper Chipezeze being pulled out after picking a first-half injury and his place taken by Talbert Shumba who was only making his fourth senior appearance for the team.
Zimbabwe had an open opportunity to get back into the game in the 54th minute, but Kadewere could not beat Mbohli one on one after being set through by Billiat’s flick-on.
His first pass aimed at Bounedjah was blocked but he picked up the pieces, drove into goal and dinked over the keeper.
Kadewere responded to Mahrez’s dink in equal measure, pulling one back for Zimbabwe in the same fashion off a brilliant Musonda through ball.