The City winger’s stinging free-kick was too hot to handle for Tunisian stopper Mouez Hassen, doubling the Desert Foxes’ lead just before the half hour in Rades.
Baghdad Bounedjah had given the visitors the lead ten minutes earlier when he found a pocket of space inside the box and volleyed home following a free-kick routine.
In a final 45 of few chances, the second half’s biggest talking point was the dismissal of substitute Adlene Guedioura.
The former Wolves, Watford and Nottingham Forest man was incredibly dismissed inside six minutes of being brought onto the pitch as a substitute in the 82nd minute, having been found guilty of two separate bookable offences.
But Djamel Belmadi’s side’s lead never looked to be under threat after a dominant opening half hour, as they limited Tunisia to just five efforts on goal throughout proceedings.
Mahrez, at his brilliant best throughout, played the full 90 for Algeria and was fully deserving of his 21st international strike.
While no points were at stake, victory at the Stade Olympique de Rades did continue the Desert Foxes’ incredible unbeaten run, as they approach that significant 30-match milestone.
They were last beaten in October 2018 by a single goal at the hands of Benin and, since then, have won 20 matches and drawn seven.
Algeria’s highly successful international break, in which they have won all three of their matches thus far, concludes with the visit of Burundi on Wednesday 16 June.
In three months’ time, attentions then turn back to reaching the 2022 World Cup, with Djibouti up first in Group A of their second round qualification group.