And, just as with his other five World Cup appearances, Schurrle had achieved the feat after coming on as a substitute.
Mourinho will be hoping Schurrle can produce more of the same next season and was delighted to be able to call his own player a world champion.
"I can also say my player is a world champion and he was involved in the move for Gotze's goal," the Chelsea boss told Yahoo Sports.
"The Chelsea family is all very proud of him."
The 51-year-old felt Lionel Messi was equally praiseworthy, despite playing on the losing side in the final.
Instead of seeing the Barcelona player as a scapegoat, Mourinho questioned Alejandro Sabella's tactics - in particular the decision to bring Serio Aguero on for Ezequiel Lavezzi at half-time.
"Argentina had been playing with two lines of four, with Enzo Perez closing Phillipp Lahm and Lavezzi doing the same on the other side," he said.
"Because they were so compact Messi could walk while defending and then when he got the ball he had the energy to make the difference.
"When Sabella brought Aguero on for Lavezzi, Argentina changed from a 4-4-2 to a 4-3-3 and they lost a lot of balance. Messi had to run much more after Lavezzi went off.
"The team lost balance and especially energy - energy that they needed in extra-time."