Gervinho scored twice and set up another goal for new signing Juan Iturbe as Roma raced to a four-goal lead in just over half an hour against the Russians, who were well out of their depth at the Stadio Olimpico.
Totti, starting his 23rd season at his only professional club, orchestrated the win, spraying passes around effortlessly from midfield in the Group E match.
There were ugly scenes in the second half as CSKA fans let off flares in the stands and fought with stewards, before riot police were called in to stop the trouble.
Italian media also reported problems outside the stadium, showing photographs of smashed car windows and unconfirmed reports said that two people were taken to hospital with stab wounds.
Roma, back in the Champions League for the first time since 2010/11, got off to a flying start when Gervinho created an opening for Iturbe and the 20 million euro (15.82 million pounds) signing from Verona slotted past Igor Akinfeev in the sixth minute.
Iturbe returned the compliment four minutes later as he picked out Gervinho and the Ivorian produced some nifty footwork to fire home the second.
Ten minutes later, Maicon got behind the CSKA defence on the right and scored with a shot which slipped through the demoralised Akinfeev's hands.
Totti set Gervinho free with an exquisite first-time pass and the Ivorian cut inside his marker, leaving him sprawling on the pitch, before firing the fourth after only 31 minutes.
CSKA suffered another defensive disaster when Sergei Ignashevich headed past Akinfeev five minutes after halftime, although the Russians pulled themselves together after that.
Ahmed Musa pulled one back with eight minutes left, the first goal Roma have conceded this season.
The only dampener for Roma was when Iturbe limped off with an injury midway through the first half.
(Writing by Brian Homewood in Berne; editing by Toby Davis)
