Everton boss Moyes: Gravesen didn't need convincing
With the game poised at 1-1, Gravesen came on just after the hour and turned the tide Everton's way as Bolton had previously dominated the match at the Reebok Stadium.
"For the first time I knew there were people behind me I could bring on and change the game from the bench," said Moyes.
"We haven't had that in Everton an awful lot, but today I was able to look around and see if we could alter the game slightly.
"We had forwards and midfielders on the bench, people who could create teams, and in the end Tommy came on and he was a calming influence. He was the big difference."
Referring to Gravesen's deadline-day move, Moyes added: "He didn't take much convincing to come back.
"I just said to him that's probably the first time supporters have chanted his name in three years.
"But we know all about Tommy, and he knows he has come here to compete for a place and he is happy with that.
"We need to get him as fit as we can to play in the Premier League, but you can see the difference he made, while he helped others with chances."
The game started perfectly for new £11.25million club record signing Ayegbeni Yakubu when he tapped home the opener in the 11th minute after sterling work by strike partner Andrew Johnson.
Bolton then controlled the game, but had to wait until the 55th minute for the equaliser when Nicolas Anelka volleyed home.
Then came Gravesen's introduction, with the home side ultimately slumping to their fourth defeat in five league games.