The 32-year-old midfielder had not scored since December 2010 before sliding home from close range in Everton's 1-1 draw with Blackburn Rovers.
The Australian was visibly delighted with his goal as his teammates raced to celebrate with him. Moyes, however, claimed that he knew his player would end the goalless run after recent good form.
"He's been playing well in recent weeks," said the Scot.
"He's looking more likely to score and I can see that in the way he's been training and the way he plays the games."
Everton are currently sitting in 14th place in the Premier League table.