The City winger was replaced by former West Ham man Sofiane Feghouli with 15 to play in Douala as the Desert Foxes’ prospects of securing one of five African World Cup qualification spots were handed a major boost.
Ex-Leicester forward Islam Slimani proved the difference, rising highest to head home Youcef Belaili’s free-kick on the stroke of half-time.
Chances were few and far between in a cagey affair, with both teams taking part in their first competitive fixtures since January’s Africa Cup of Nations.
The two sides experienced contrasting fortunes at the tournament, with Mahrez and co.’s defence of the trophy ending at the group stage, while host nation Cameroon bowed out in the semi-finals following a penalty shootout defeat to Egypt.
But it was Djamel Belmadi’s side who enjoyed the majority of the play, with Slimani testing the reflexes of host stopper Andre Onana inside 15 minutes.
And the duo’s running battle continued, with Slimani eventually coming out on top in the game’s crucial moment.
The 33-year-old’s header was too powerful for Onana to push away from danger, with the goalkeeper tipping the ball onto the underside of the bar and into the net despite getting a strong hand to it.
Algeria went close to a second deep into stoppage time when Ishak Belfodil’s effort flashed just wide of the far post, but Mahrez and co. had to settle for a one-goal margin.
Victory means the Desert Foxes take a crucial advantage into Tuesday’s second leg in Blida and, should they avoid defeat, they will secure their spot in Qatar and qualify for the World Cup for just the fifth time in their history.
Meanwhile, Taylor Harwood-Bellis and Tommy Doyle both started for England Under-21s as they cruised past Andorra in European Championship qualifying.
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Stoke City loanee Harwood-Bellis captained the side at Bournemouth’s Vitality Stadium while Doyle, who is on loan at fellow Championship side Cardiff City, started in midfield.
Folarin Balogun snuck an early opener in at the near post to set Lee Carsley’s youngsters on their way, before Jacob Ramsey doubled the advantage on 35 minutes.
Morgan Gibbs-White added a third before the hour, but Albert Rosas landed an unlikely response for the visitors just nine minutes later.
But the Young Lions’ three-goal lead was restored with ten to play through substitute Anthony Gordon, ensuring Harwood-Bellis, Doyle and co. made it four wins from five in their bid for Euro U21 Championship qualification.
