Vladimir Petkovic’s side were eager to prove themselves as AFCON contenders after a chequered recent history in the competition, and Mahrez broke the deadlock in just the second minute.
The former Manchester City forward fired home a fine left-footed finish past Monged Elneel after Hicham Boudaoui backheeled the ball into his path to score his seventh AFCON goal, moving one clear of Lakhdar Belloumi.
Nonetheless, Sudan’s response was encouraging, as Yaser Awad was twice denied by Luca Zidane after being played through down the right-hand side.
The Desert Warriors would have hoped to kick on from their early opener, but were left toiling for the remainder of the first half against James Kwesi Appiah’s well-drilled outfit.
The Falcons of Jediane were threatening to level the scores before half-time, but their hopes of a comeback suffered a major blow when Salaheldin Alhassan was shown a second yellow card for a challenge on Rayan Ait-Nouri.
Algeria were looking to put the game to bed after the break, as chances fell to Fares Chaïbi and Baghdad Bounedjah, but it was Mahrez who struck again to give the Desert Warriors breathing space.
The 34-year-old expertly took Mohamed Amoura’s pass into his stride before coolly dispatching his subsequent strike past Monged.
The Sudan shot-stopper kept the deficit at two moments later with a fine save to deny Amoura, before the Wolfsburg forward cannoned the post with a separate volley.
However, there was still time for Ibrahim Maza to round off the scoring with a well-taken close-range finish after Bounedjah headed the ball into his path.
Ultimately, Algeria didn’t really have to move out of second gear to claim all three points against a Sudan team whose appearance at the finals is truly remarkable in itself. A country blighted by civil war had their moments in this contest, but unsurprisingly failed to significantly trouble Petkovic’s team.
The Desert Warriors face a much stiffer challenge when they face Burkina Faso on Sunday, while Sudan turn their attention to a clash against Equatorial Guinea the same day.
Flashscore Man of the Match: Riyad Mahrez (Algeria)
Check out the match summary with Flashscore
