The visitors, who lost their opening game of the season 1-0 at home to Krilya Sovetov, took the lead some 60 seconds after kick-off, Macedonian international Goran Maznov finding the back the net after a corner.
CSKA, who were knocked out of the UEFA Cup after a 2-0 defeat in Ukraine to Shakhtar Donetsk on Thursday, were clearly rattled, and Tomsk could have had a second in the 12th minute, Hungarian midfielder Norbert Nemeth hitting the bar.
The escape seemed to sting CSKA into action, and Chelsea target Yuri Zhirkov replied with a shot that came back off the post two minutes later.
Tomsk then weathered a CSKA storm and went into the break still ahead, but it looked as if the Muscovites' class would tell in the second 45 minutes.
CSKA could have equalized when Zhirkov went one-on-one with the keeper in the 54th minute, and should have leveled but for a rare Vagner Love miskick in front of goal in the 73rd as the former Red Army team came forward time and time again.
As the minutes ticked away, CSKA threw caution to the wind in search of an equalizer, but the Siberian side, with a little bit of luck, stood firm to come away from the Russian capital with three unexpected points.
Table (two games played)
Dynamo Moscow - 6
Krilya Sovetov - 6
Rubin - 4
Zenit St. Petersburg - 4
Terek Grozny - 4
CSKA Moscow - 3
Kuban - 3
Tom Tomsk -3
Lokomotiv Moscow -2
Rostov - 2
Khimki - 1
Spartak Moscow - 1
Amkar - 1
FC Moskva - 1
Spartak Nalchik - 0
Saturn - 0
