Cameroon striker Eto'o put the home side ahead with a clinical finish just before the break, taking advantage of a nice feed by Ivory Coast international Traore.
Eto'o, who joined wealthy Anzhi from Inter Milan last September, returned the favour in the 62nd minute, setting up Traore's winner three minutes after Volga's equaliser.
"Today we had an extra motivation to win because we knew that CSKA had already lost their match," Dutchman Hiddink, who guided Russia to the Euro 2008 semi-finals, told reporters.
"Now we are the top team in such a strong league as Russia. This is a very important step for our club."
The only problem for Anzhi on Sunday was the injury to starting goalkeeper Yevgeny Pomazan, who was forced to leave the game with a suspected broken rib early in the first half and will now miss Thursday's Europa League game against Swiss side Young Boys.
CSKA not only dropped valuable points in the heated Moscow derby but also lost their most creative player - Russia midfielder Alan Dzagoev - who was red-carded in the second half for lashing out at Dynamo's Australia international Luke Wilkshire.
Leading striker Alexander Kerzhakov was also demoted to the reserves for "improper behaviour" before being recalled after making peace with Zenit's Italian coach Luciano Spalletti.
