The Manchester City winger looked to have scored the winner when he nutmegged a defender with a composed close-range finish that found the bottom corner 23 minutes from time, but Diego Lainez netted a late leveller for the hosts.
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Mahrez had been involved in Algeria’s opener as he combined with Sofiane Feghouli, who teed up Ismaël Bennacer for a 20-yard drive two minutes after Jesus Manuel Corona had put Mexico ahead.
The Desert Warriors were forced to play with 10-men for the majority of the second half after Adlène Guedioura was dismissed for a second bookable offence.
Elsewhere, it was a frustrating night for the Spanish trio of Rodrigo, Ferran Torres and Eric Garcia as they lost 1-0 to Ukraine in the UEFA Nations League.
Rodrigo played the full 90 minutes, while Torres was introduced on the hour mark but neither could inspire Luis Enrique’s side to victory in a match they dominated.
Spain enjoyed 72% of possession and had 21 shots to Ukraine’s two, but the hosts snatched victory when Viktor Tsyhankov fired emphatically past David De Gea to complete a slick counter-attack.
Garcia was an unused substitute, whilst Oleksandr Zinchenko was not involved as he stayed at home during the international break due to injury.
Despite their first loss, Spain remain top of UEFA Nations League Group A4, with seven points from four games. Ukraine sit third on six points and behind Germany on goal difference.
Meanwhile, Ederson was an unused substitute as Brazil beat Peru 4-2 in a World Cup qualifier.
More City players may be in action on Wednesday evening, when England, the Netherlands and Portugal are all due to play.
Kyle Walker, Nathan Ake, Joao Cancelo, Ruben Dias and Bernardo Silva could all be involved for their respective countries, though Kevin De Bruyne will not feature for Belgium after he withdraw from the squad on Wednesday.
