Belgium's World Cup goalkeeper Courtois, who has spent the last three seasons on loan at Liga champions Atletico Madrid, returned to Stamford Bridge insisting he would play, or leave.
The 22-year-old has been preferred to Czech Republic goalkeeper Petr Cech, 32, who has played 470 senior matches for Chelsea.
Mourinho had earlier said that he possessed two if the best three goalkeepers in the world, referring to Bayern Munich and Germany star Manuel Neuer, widely regarded as the top player in his position.
After the match the Chelsea boss insisted Cech would fight for his place and that he wanted both keepers at the club.
But the decision to use Courtois means Cech, who was last season's Premier League goalkeeper of the year, may seek a transfer.
There were also debuts for big-money signings Costa and Cesc Fabregas, the Spain duo having joined from Atletico and Barcelona respectively.
Fellow new signings Didier Drogba, Filipe Luis and Kurt Zouma were on he bench, with Drogba coming on for his second Chelsea debut, having returned to the club two years after winning them the Champions League.
- Sports & Recreation
- Petr Cech
- Atletico Madrid
- Diego Costa
- Branislav Ivanovic