The Toffees were struggling to break the Germans down but managed to do so twice in the final eight minutes, after Moyes had decided it was time to send on Victor Anichebe - despite the young striker's broken hand.
The result was a penalty, Anichebe wrestled to the ground as he raced goalwards - and then the Nigerian-born player made it 2-0 to give Everton two wins out of two at the top of Group A.
"What a way to finish! Victor came on and made such an impact," said a triumphant Moyes.
"I was worried about putting him on, because he has a broken hand - but what do I know?
"I thought it was a good performance. For long periods, we did well enough."