Eto'o left Schalke goalkeeper Timo Hildebrand red-faced after 31 minutes at Stamford Bridge when the experienced German's attempted clearance hit the striker and rolled into the net.
The former Valencia and Sporting Lisbon custodian took far too long to clear the ball and Schalke never recovered from his howler.
Eto'o scored his second of the night after the break and Demba Ba came off the bench to seal a 3-0 win that puts Chelsea firmly on course to progress from Group E, following their failure to reach the knockout stages last season.
Mourinho had advised Eto'o to put pressure on Hildebrand when he had the ball at his feet and the Portuguese was delighted to see his words of wisdom pay off.
The Chelsea manager said: "I told him that. I know the keeper from Portugal and Spain because he was there and we know Schalke likes to play back passes and play from the back with the keeper so Samuel was clever in the way he closed him down."
Chelsea suffered a 2-0 Premier League defeat at Newcastle United on Saturday and Mourinho was pleased with his team's response after making six changes to the starting line-up.
He added: "I think it was a good [response] but of course the first 15 minutes were difficult; we were a team without big maturity and stability after the defeat on Saturday.
"After that we played very well and kept possession in a comfortable way and after the first goal we played well.
"I know Petr Cech made a fantastic save for a possible 1-1 but everybody worked hard and made defensive work, especially the wingers against their full-backs."
