Moloney successfully argued that the contact with Logan was negligent and not reckless, downgrading the charge from a two-match suspension to a reprimand and 93.75 demerit points.
Moloney is now free to play his 100th AFL match this round.
The incident occurred late in the final term at TIO Stadium on Saturday night, minutes before Melbourne hung on for a thrilling one-point win.
The Demon leader was delighted to have his initial penalty downgraded.
"It was a good result," Moloney said. "It's my 100th game against my old team Geelong, so I'm really looking forward to that now.
"I was a bit nervous early in the week, but now I can just concentrate on the Cats on Saturday."
During the hearing Moloney was adamant he did not make head-high contact with Logan's head. He was certain he made "shoulder-to-shoulder" contact.
A medical report was supplied from Port Adelaide medical officer Mark Fisher, which said: "The player underwent no treatment … and is fit to play next week."
The tribunal found that it was head-high contact but found the conduct to be more reckless than negligent.
