The City winger had a great chance to put his side ahead in the 10th minute, but directed his shot wide, before turning provider soon afterwards for Sofiane Feghouli, who also failed to find the target.
The winner finally arrived in the 83rd minute, when Mahrez swung a delicious free kick into the box from deep on the right that was met by former Liverpool man Carl Medjani.
Next up for the Desert Foxes are back-to-back games against Malawi in the October international break.
Elsewhere City skipper Wes Morgan was given the honour of leading Jamaica as they were edged out by Canada in a Toronto friendly.
The Reggae Boyz took the lead when Kemar Lawrence netted from a 30th minute free kick, but just a minute later the hosts were level when former Newcastle man David Edger got on the end of a set play.
After the break a number of chances went begging for Jamaica before Marcel DeJong’s free kick and another from Tosaint Ricketts sealed the win.
Over in Togo, Jeff Schlupp’s Ghana continued their African Cup of Nations qualifying campaign in Group E with a battling win over Togo.
The Black Stars edged a five-goal thriller 3-2 to move second in the group after two games, but were behind after just 12 minutes to a Floyd Ayite goal.
Skipper Asamoah Gyan levelled with a header soon afterwards and Emmanuel Agyemang Badu then put them ahead with another good strike.
However with just over 10 minutes left, Tottenham Hotspur striker Emmanuel Adebayor made it 2-2 and looked to have secured a point until Christian Atsu scored on 85 minutes to seal the win.
City’s international contingent will now re-join their team-mates ahead of the weekend’s Barclays Premier League clash with Stoke City at the Britannia Stadium.
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