The Premier League champions won after Loic Remy scored from just inside the box in the 30th minute after an Eden Hazard assist.
Mourinho selected a strong team for the game in front of 83,598 fans??at the Olympic Stadium in Sydney, but gave youngsters including Ruben??Loftus-Cheek and Nathan Ake a chance to impress.
Mourinho told Chelsea FC afterwards: ???We still wanted to play for a result and we don???t like to lose. Even though some of the players are tired, you can see the mentality is still there until the last second of the season.
???We owe it to the fans [to play a strong side] ??? you see 80,000 people here with their shirts and supporting our team.
“We had lots of chances to have a different score and in the last part of the game the kids lost a little control and Sydney could almost get a draw, which would???ve been fantastic for them.???
Mourinho also enjoyed a far friendlier time on the touchline with opposite number, Graham Arnold, than he tends to afford his Premier League counterparts.
He was seen swapping coats with the Australian manager and has invited him to visit the Chelsea training ground.
He added: ???We met yesterday, and we spent time together again today. We shared some ideas and he wants to come to Cobham for a couple of weeks too.???