Oleg Vlasov grabbed the only goal at Stadion Start as Saransk followed in the footsteps of Terek Grozny by overcoming Andre Villas-Boas' table-toppers this term.
The result continued a disappointing run for Zenit, who have now suffered losses in five of their last nine fixtures in all competitions.
However, Zenit remain well clear at the top of the table, with Krasnodar five points adrift and CSKA Moscow seven behind.
CSKA did produce the most eye-catching performance of the weekend, however, when cruising to a 5-0 triumph over Ufa.
Zoran Tosic was the star, his double coming as well as goals from Bibras Natkho, Seydou Doumbia and Ahmed Musa.
Krasnodar wrapped up the round of fixtures with a 1-0 success at Terek Grozny on Sunday, Wanderson hitting the decisive goal.
Another side riding the crest of a wave are Lokomotiv Moscow, who continue to look formidable under boss Miodrag Bozovic.
Bozovic has shown a Midas touch since taking the reins, overseeing a run of four wins and two draws.
The latest of those victories was among the biggest, with Alan Kasaev grabbing the only goal to edge out city rivals Spartak Moscow on Sunday.
The capital's other two sides both drew 1-1, Torpedo Moscow earning a point at Kuban Krasnodar and Dinamo Moscow doing likewise against Rubin Kazan.
Arsenal Tula remain at the foot of the table following a 2-1 home loss to FC Ural, while Rostov are a place better off having drawn 1-1 with Amkar Perm.