Mauricio Pereyra put Oleg Kononov's side on course for victory over their local rivals when he opened the scoring after 21 minutes at the Kuban Stadium.
The home side denied their neighbours all three points though, as Gheorghe Bucur struck 13 minutes into the second half and neither side could fashion a winner.
CSKA Moscow are above Kononov's men on goal difference following their 2-1 home victory over struggling Amkar Perm' on Tuesday.
The champions left it late to secured a second successive victory, with Roman Eremenko scoring his second goal of the game in stoppage time after the visitors had led for much of the game following Soslan Takazov's opener.
Leaders Zenit, meanwhile, responded to their surprise defeat at Mordovia Saransk on Saturday by securing a 1-0 win at Rubin Kazan.
Belgium midfielder Axel Witsel proved to be the match-winner for Andre Villas-Boas' side, who now hold a seven-point lead at the summit.
There was more misery for bottom side Arsenal Tula, as Haris Handzic's first-half effort consigned them to a 1-0 home defeat against Ufa.
Arsenal are now three points adrift at the bottom after Rostov secured a 1-1 draw with Spartak Moscow on Thursday.
Rostov took the lead 19 minutes from time when Dmitri Torbinski was on target, but they were denied all three points after Denis Glushakov replied four minutes later.
Fourth-placed Dinamo Moscow were 1-0 winners at Mordovia Sarans in the other game to be played on Thursday, while Torpedo Moscow also won on the road as Terek Grozny were beaten 1-0 on Wednesday.
Lokomotiv Moscow ran out 1-0 winners over Ural in the other game to be played on Wednesday.
