Juan Iturbe, Gervinho and Francesco Totti had all been named among the substitutes for Sunday's 1-0 Serie A win at Empoli, but two of them found the net in a dominant Group E display at the Stadio Olimpico.
Iturbe broke the deadlock after being sent through on goal by Gervinho, before the former Arsenal man got his name on the scoresheet four minutes later.
Maicon's third will have goalkeeper Igor Akinfeev wincing when he watches the highlights, and Gervinho doubled his tally before the break after being picked out on the right wing by Totti.
A dismal performance got worse for CSKA five minutes into the second half, when Sergei Ignashevich put the ball into his own net and although Ahmed Musa bundled home later on, the damage had long since been done..
The result represents Roma's biggest-ever win in the competition as they made a statement of intent.
Garcia's men looked dangerous from the first whistle and took the lead in the sixth minute.
Gervinho was the architect, slicing the CSKA defence open with an incisive throughball that left Iturbe to simply prod beyond Akinfeev.
The roles were reversed four minutes later, when Gervinho collected an Iturbe pass in the centre of the penalty area and composed himself before doubling the hosts' advantage with a poked effort.
Seydou Doumbia surged forward in the 16th minute as CSKA sought to reduce the deficit, but the Ivory Coast international inexplicably tripped while bearing down on goalkeeper Morgan De Sanctis.
Maicon added a third in the 20th minute, when he found himself in acres of space on the right and moved into the penalty area before powering home through the weak hands of Akinfeev – evoking memories of a similar howler by the goalkeeper for Russia at this year's World Cup.
There was some concern for Roma when Iturbe limped off in the 25th minute, but Gervinho soon brought the smiles back to the faces of the home fans by once again exposing the dreadful visiting defence – deceiving Ignashevich with a neat pull-back and then firing in a left-footed effort.
Miralem Pjanic could have made it five before the break, but his shot was met with an excellent one-handed save by Akinfeev.
There was no let-up from Roma at the beginning of the second half, and Ignashevich headed into his own net from a Pjanic cross to pile on the misery after 50 minutes.
Doumbia shot into the side-netting and hit the crossbar in quick succession in a vain attempt to produce an unlikely fightback, before play was stopped temporarily as flares were thrown from the stands.
Musa's solitary late strike - a chip over De Sanctis - will have done nothing to lift the spirits of the travelling fans and although Georgi Schennikov also hit the crossbar, the Russian outfit were outclassed and will be eager to put their Roman rout behind them.
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