Slimani stars for Algeria, disaster for Mali's Sissako
Slimani, 33, soared in a crowded goalmouth to head a Youcef Belaili free-kick powerfully past goalkeeper Andre Onana into the roof of the net.
Even 11 minutes of added time could not bring Cameroon an equaliser and they must win in Blida on Tuesday to avoid missing successive World Cups.
Cameroon hold the record for World Cup appearances by an African nation with seven and have not missed two in a row since first qualifying in 1982.
Success was particularly sweet for Algeria as they fared disastrously in the Atlantic port city of Douala when defending the Africa Cup of Nations title two months ago.
Algeria began the tournament boasting a 34-match unbeaten record only to draw with Sierra Leone and lose to Equatorial Guinea and the Ivory Coast to make a humiliating first-round exit.
In Bamako, Mali defender Moussa Sissako conceded an own-goal and was sent off within four minutes as they lost 1-0 to Tunisia and now stand little chance of going to the World Cup for the first time.
Under pressure from Seifeddine Jaziri, Sissako pushed the ball toward his own goal on 36 minutes, unaware that goalkeeper Ibrahim Mounkoro had strayed off his line, and the ball landed in the net.
When Sissako committed a last-defender foul on Jaziri soon after he was shown a red card and although Mali created the better second-half chances, they failed to convert any into goals.
Sad debut for Doucoure Mali gave a first cap to France-born Everton midfielder Abdoulaye Doucoure, who had long hoped to play for his country of birth before agreeing to represent the homeland of his parents.
In Kinshasa, Tarik Tissoudali scored a brilliant equaliser as Morocco moved closer to a sixth World Cup appearance by drawing 1-1 with the Democratic