Roberto Carlos opens account for Makhachkala
The 38-year-old, a member of the 2002 World Cup-winning team, converted a penalty to put the visitors ahead in the 58th minute against Dynamo Moscow.
Dynamo, who had Russian international Igor Semshov sent off for handling in the box moments earlier, twice came from a goal down to draw 2-2.
Bosnia playmaker Zvjezdan Misimovic secured a point for the home side with a penalty two minutes from time.
The draw lifted Anzhi into sixth place with nine points from six matches while Dynamo, who last week sacked Montenegrin coach Miodrag Bozovic after being knocked out of the Russian Cup, are ninth with eight points.
Champions Zenit St Petersburg lead the way with 13 points following a 3-0 win over lowly Krylya Sovietov Samara on Sunday.