After clinching the title by just two points last season, CSKA were looking to make a statement of intent as they began their title defence away at the Stadion Central'nyj on Wednesday.
And things were looking good when Nigerian Ahmed Musa put them into a 24th-minute lead.
But the title holders were left shocked by their unfancied opponents in the second half when a double from Spartak Gogniev came them a 2-1 advantage.
WIth time running-out, it was left to Brazilian striker Vagner Love to rescue a point with just four minutes remaining.
Zenit St Petersburg are looking to reclaim the title they surrendered to CSKA and started their campaign with a 2-1 victory against Krasnodar at the Stadion Kuban on Wednesday.
Viktor Faizulin scored the opener in the 22nd minute, before Danny doubled their advantage before half-time.
Mauricio Pereyra pulled one back immediately after the re-start, but Zenit hung on to claim the points.
Guus Hiddink's Anzhi Makhachkala started their campaign with a 2-2 with Locomotiv Moscow at the Anzhi-Arena after a frantic end to the match on Sunday.
After a goalless opening period, Senegal attacker Dame N'Doye opened the scoring for the visitors just after the hour mark.
Their lead was shortlived, however, as strikes from Samuel Eto'o and Lacina Traore within the space of five minutes looked to have secured three points for Anzhi.
But with the game in injury time, former Tottenham Hotspur striker Roman Pavlyuchenko rescued a point for Locomotiv.
Amkar Perm top the table after one game, as they defeated Tom' Tomsk 2-0 at the Stadion Zvezda on Tuesday.
Two penalties from Bulgarian Georgi Peev inside the opening 10 minutes was enough to secure the three points for the home side.
Spartak Moscow, who achieved a fourth place finish last campaign, got off to a solid start with a 2-1 victory away to Krylya Sovetov at the Stadion Metallurg on Tuesday.
Alberto Costa and Yura Movsisyan sent the away side into half-time with a two goal advantage.
Luis Caballero's 61st-minute strike ensured a nervy final half-hour, but Krylya were unable to find the equaliser.
Elsewhere, Dinamo Moscow played out a 2-2 draw with Volga, Kuban' Krasnodar and Rubin Kazan shared the points as their game finished 1-1, while Rostov defeated Terek Grozny 2-1.