The 28-year-old who joined the Stamford Bridge giants from Rennes as back-up for error-prone Kepa Arrizabalaga was handed his maiden appearance in the competition against the Spanish elite division side.
He was called to action in the closing stages of the first half, denying Argentine forward Lucas Ocampos after the hosts failed to clear a cross from the far side.
For his contributions, Mendy made three saves as the former European champions kept a clean slate against Julen Lopetegui’s side who dominated ball possession in the Group E contest.
“In the three games Edouard Mendy has played since he has been here he has played very well,” the Chelsea legend told the club website.
“He made a good save today and that is two clean sheets. When he came in I said he will be great for competition.
“We knew his qualities and he has shown them, so at the moment he is first choice but that is always up for grabs and that is why you have competition.”
“Thiago Silva was very good [on Tuesday],” he continued.
“He brought both quality and experience as we hoped and he affects others around him. He was a big plus and a part in keeping the clean sheet.
“I will manage his workload this season. I have a very close relationship with him already and I remember being in that position towards the back end of my career so I will be very aware of his maintenance, training and game selection, to try to have him at his optimum.”
Following Rennes' 1-1 draw with FC Krasnodar, all teams in Group E are tied on one point after the first round of games.
Chelsea travel to face Manchester United in their next Premier League match, before returning to Champions League action with an away game against Krasnodar.