The Blues took the lead in Romania courtesy of a Ramires strike in the 20th minute, before Daniel Georgievski's own goal a minute before half time put them further in control.
Ramires added a third 10 minutes into the second period before Frank Lampard rounded off the scoring late on.
The result represented Chelsea's first points of this season's competition, after a shock 2-1 home defeat to Basel in their opening Group E encounter.
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"I think we are going to do it," he said.
"The result today is important because we had to win. The result was obviously very good.
"The performance was also very solid. We kept control of the game and result and we played good football with intelligence and maturity away from home."
The Portuguese also had special praise for Andre Schurrle, who had a hand in two of Chelsea's goals.
"Schurrle was fundamental," he added. "We identified what we had to do to penetrate their defence. He was the man for that. He was in the position where we knew we could [have success] and we played from there.
"We always had control of the game. We scored four, and probably could have scored six or seven because we played really well."
Juan Mata, like Mourinho, was pleased with the way that his side bounced back from that opening defeat against Basel.
"After the first game against Basel we needed to win today," he added.
"From the first moment we showed that we wanted to win. I think we played really well. We will take a lot from this game."
The win leaves Chelsea third in the group, level on points with Basel and three points adrift of Schalke, whom they visit on matchday three.