Andre Villas-Boas' men had to come from behind after Maxim Kanunnikov had given the home side a 10th-minute lead on Saturday, but two goals in five minutes just after the break from Domenico Criscito and Aleksandr Kerzhakov saw them take all three points.
That victory, combined with leaders Lokomotiv Moscow's 0-0 draw with city rivals Spartak on Saturday, means the 2012 champions sit just one point of the summit.
CSKA Moscow level on points with Dinamo after picking up their third straight league win on Monday.
It was a mixed day for CSKA playmaker Alan Dzagoev, who added to Zoran Tosic's fifth-minute opener before being sent off in the 41st minute.
Monday's other fixture involving Krylya Sovetov and Terek Grozny was postponed due to heavy snow.
Elsewhere over the weekend, Roman Shirokov scored twice as Krasnodar won 3-1 at city rivals Kuban Krasnodar, bottom club Anzhi's woes continued as they lost 2-1 at Ural, and Rostov picked up a 2-1 win at Rubin Kazan.
