Reigning champions CSKA edged a tight affair at Arena Khimki 1-0, claiming the crucial winner when Ahmed Musa struck in the 33rd minute.
Dinamo were indebted to two late goals for their 3-1 win at Torpedo, and Stanislav Cherchesov's men now sit second in the table behind leaders Zenit.
Aleksey Ionov put the visitors in front after 10 minutes, but Dinamo's response was immediate as Aleksandr Katsalapov levelled a minute later.
In the final 10 minutes, Dinamo eventually prevailed as Ionov grabbed his second and then Balazs Dzsudzsak rounded off the scoring a minute from time as the visitors claimed the bragging rights.
At the summit, Zenit continued their dominant start to the season with a 5-0 thumping of struggling Rostov, taking their tally to a maximum 24 points from eight matches.
Salomon Rondon helped himself to a hat-trick, taking his league tally for the season to seven goals, while the leaders had a helping hand from their beleaguered hosts, who contributed further to their own misery as both Siyanda Xulu and Vitaliy Djakov put through their own net.
Rostov are now second from bottom - and in an automatic relegation berth - after Ural gained their first win of the campaign with a 1-0 triumph at Ufa thanks to Alexandr Erokhin's 42nd-minute winner.
Newly promoted Arsenal Tula's woes in their new surroundings continued as they went down 1-0 at home to Mordovia Saransk, who were second-tier champions last season.
Substitute Ruslan Mukhametshin struck the winner 20 minutes from the end and Arsenal Tula remain rooted to the foot of the table with just one point to their name from eight matches.
Kuban Krasnodar came from behind to defeat Rubin Kazan 2-1 at home, while Krasnodar triumphed by the same scoreline away at Amkar Perm.
Elsewhere, Jose Manuel Jurado's stoppage-time equaliser earned Spartak Moscow a point in a 1-1 draw with Terek Grozny, who had gone in front through Mauricio.
