The club's remarkable fall from grace since seeing their budget drastically slashed has seen them drift from back-to-back UEFA Europa League campaigns to now being all but relegated from the Premier League.
And despite their creditable away draw at the weekend, guaranteed safety is now beyond the reach of Anzhi, who once boasted players such as Samuel Eto'o, Willian and Roberto Carlos.
Anzhi are also eight points adrift of a place in the relegation play-offs with just three matches left to play.
Artem Dzyuba put Rostov in front with his 16th league goal of the season, before Diniyar Bilyaletdinov made the most of Alexandru Gatcan's dismissal and pulled the visitors level 10 minutes from time.
Rostov were reduced to nine men late on when Florent Sinama-Pongolle was shown a straight red card.
At the other end of the table, Zenit kept just ahead of second-placed Lokomotiv Moscow with a 2-0 win over second-bottom Volga.
Goals from Axel Witsel and Viktor Faizulin proved enough to keep Zenit a point ahead of Lokomotiv, who were 3-1 winners at Krasnodar.
The game looked to be heading for a draw until Alexandr Samedov atoned for his earlier penalty miss to score a stoppage-time brace and keep his side's title tilt alive.
Along with Zenit, third-placed CSKA Moscow are the division's form club with seven wins on the bounce.
The latest came in the shape of a 2-1 triumph over Rubin Kazan, with Seydou Doumbia netting the winner from the penalty spot eight minutes into the second half.
Spartak Moscow were unable to capitalise on city rivals Dynamo's 1-0 defeat at Terek Grozny as they slipped to a 2-0 home defeat to Kuban Krasnodar on Monday.
Elsewhere, Ural failed to widen the gap between themselves and the relegation play-off zone as they drew 0-0 at home against fellow strugglers Tom Tomsk, while Krylya Sovetov squandered a 2-1 lead as they were held to a 2-2 draw by Amkar Perm.
