Strikes from Philippe Mexes and Marco Borriello either side of the 70th-minute mark helped Claudio Ranieri’s men secure a 2-1 success over their Romanian opponents in the Group E clash at the Stadio Olimpico.
The result comes after a moral-boosting league win over reigning Italian champions Inter Milan last weekend.
Roma had failed to win any of their opening five games this season, including a disappointing 2-0 reversal against Bayern Munich in their first European match of the 2010-11 campaign.
However, their success over Cluj has propelled the Italian side to second in Group E behind last year’s beaten finalists.
“Beating Cluj was an important result for everything and everyone,” said Totti. “(They are) three crucial points that bring us fully into play in our Champions League group.”
He added: “In football the best medicine is always the win.”